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<div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</d我v> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#results">结果</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#discussion-and-conclusion">讨论和结论</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#appendix">附录</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abbreviations">缩写</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#data-availability">数据可用性</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#conflicts-of-interest">的利益冲突</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#authors’-contributions">作者的贡献</一个> <a 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class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2022/3616163" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2022/3616163</一个></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</button> </div> <h1 class="articleHeader__title">预测的鲁棒性大的现实世界的社交网络使用机器学习模型</h1> <div class="articleHeader__authors"> <span class="articleHeader__authors_author">Ngoc-Kim-Khanh阮<一个href="https://orcid.org/0000-0003-3542-0518" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a>,<sup>1</sup></span> <span class="articleHeader__authors_author"><strong>Quang阮</strong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><a href="https://orcid.org/0000-0002-1188-3385" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a>,<sup>2、3、4</sup></span> <span class="articleHeader__authors_author">Hai-Ha范教授,<sup>5</sup></span> <span class="articleHeader__authors_author">Thi-Trang勒,<sup>4</sup></span> <span class="articleHeader__authors_author">Tuan-Minh阮,<sup>4</sup></span> <span class="articleHeader__authors_author">大卫。Cassi<一个href="https://orcid.org/0000-0001-6072-5255" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a>,<sup>6、7</sup></span> <span class="articleHeader__authors_author">弗朗西斯科·Scotognella,<sup>8、9</sup></span> <span class="articleHeader__authors_author">罗伯特·Alfieri,<sup>6、7</sup></span> <span class="articleHeader__authors_author">和米歇尔Bellingeri<一个href="https://orcid.org/0000-0002-5729-1123" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a><sup>6、7、8</sup></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</button> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</strong> <span>安德里亚Murari</span> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</strong> <span>2022年6月30日</span> </div> <div class="articleHeader__timeline_item "> <strong>修改后的</strong> <span>2022年9月24日</span> </div> <div class="articleHeader__timeline_item "> <strong>接受</strong> <span>2022年10月3日</span> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</strong> <span>2022年11月09</span> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>计算网络的鲁棒性,即。,the capacity of a network holding its main functionality when a proportion of its nodes/edges are damaged, is useful in many real applications. The Monte Carlo numerical simulation is the commonly used method to compute network robustness. However, it has a very high computational cost, especially for large networks. Here, we propose a methodology such that the robustness of large real-world social networks can be predicted using machine learning models, which are pretrained using existing datasets. We demonstrate this approach by simulating two effective node attack strategies, i.e., the recalculated degree (RD) and initial betweenness (IB) node attack strategies, and predicting network robustness by using two machine learning models, multiple linear regression (MLR) and the random forest (RF) algorithm. We use the classic network robustness metric<我>R</我>作为模型反应和8网络结构指标(NSI)作为预测变量和大型数据集训练的48个真实的社交网络,节点的最大数量是265000。我们发现射频模型可以预测网络的鲁棒性与均方误差(RMSE)为0.03,比30%高模型。在结果中,我们发现RD策略效果比IB攻击现实世界的社交网络。此外,高表明,最重要的因素来预测网络的鲁棒性是无标度指数<我>α</我>和平均节点度<<我>k</我>>。相反,RF表明assortativity程度<我>一个</我>,全球亲密,平均节点度<<我>k</我>>是最重要的因素。这项研究表明,机器学习模型可以是一个有前途的方法来推断社交网络的鲁棒性。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>社交网络的研究从复杂性科学的角度吸引了很多最近的兴趣(<一个href="#B1">1</一个>]。特别是研究的动态过程,发生在这些复杂网络可以有各种各样的应用程序。例如,网络鲁棒性的研究,即,“network robustness” is the capacity of a network to hold its functionality when a proportion of nodes/edges are removed, can help attack a network efficiently, or inversely design a more robust network structure in practice [<一个href="#B2">2</一个>- - - - - -<一个href="#B7">7</一个>]。另一方面,研究流行过程,发生在网络可以用来传播新闻(<一个href="#B8">8</一个>- - - - - -<一个href="#B12">12</一个>),优化疫苗接种策略<一个href="#B13">13</一个>- - - - - -<一个href="#B15">15</一个>),或者定义一个更好的社会距离规则(<一个href="#B16">16</一个>- - - - - -<一个href="#B19">19</一个>]。</p> <p>除了一些简单的模型网络分析模型可以开发(<一个href="#B20">20.</一个>- - - - - -<一个href="#B24">24</一个>),大多数的研究依赖于计算机模拟。例如,网络的鲁棒性,研究节点/边删除蒙特卡罗模拟通常采用。在这样一个过程中,节点/边使用电脑模拟顺序从网络中删除。“鲁棒性”指标然后记录删除过程的每一步。最常用的鲁棒性度量是最大的连接组件(LCC)的网络(<一个href="#B25">25</一个>]。</p> <p>要删除选中节点/边的方式叫做删除策略或攻击策略。人能攻击策略分为两类型进行分类,初步和重新计算攻击策略。首次攻击策略,节点/边被删除节点/边排名提前去除模拟计算。重新计算攻击策略相比,每个节点/边切除后的排名更新(<一个href="#B4">4</一个>]。</p> <p>删除节点的攻击策略,节点排名通常是计算使用节点中心度等措施(<一个href="#B26">26</一个>,<一个href="#B27">27</一个>,亲密<一个href="#B4">4</一个>,中间状态(<一个href="#B7">7</一个>,<一个href="#B30">30.</一个>]。发现,社交网络,重新计算介数节点攻击策略(RB)是,平均而言,最有效的节点攻击策略拆除网络(<一个href="#B2">2</一个>,<一个href="#B7">7</一个>,<一个href="#B28">28</一个>,<一个href="#B29">29日</一个>]。其他有效的策略重新计算程度(RD)和最初的中间性(IB) [<一个href="#B7">7</一个>,<一个href="#B28">28</一个>,<一个href="#B30">30.</一个>]。</p> <p>因为顺序删除过程的本质,节点删除模拟计算昂贵,特别是对于重新计算策略。例如,模拟使用RD攻击策略的时间复杂度<我>O</我>(<我>N</我>×<我>E</我>),<我>N</我>节点和数量吗<我>E</我>是网络的边的数量。原因是节点删除过程有一个<我>N</我>一步,每一步,一定程度排名计算一次尺度<我>E</我>。然而,对于RB,整个网络的计算计算中间状态是非常昂贵的,由于网络的节点介数的定义(<一个href="#B31">31日</一个>,<一个href="#B32">32</一个>]。已知最有效的算法计算网络中间性Brandes算法(<一个href="#B33">33</一个>),时间复杂度为O (<我>N</我>×<我>E</我>)。结果,整个节点删除过程使用IB和RB攻击策略的时间复杂度O (<我>N</我>×<我>E</我>)和O (<我>N</我><sup>2</sup>分别×E)。尽管IB攻击策略相同的时间复杂度RD攻击策略,RB的时间复杂度要高得多。例子,在图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig1/" target="_blank">1</一个>,我们现在总模拟时间tIB, tRD相应的攻击策略IB和RD,分别为我们所有的研究社交网络(48网络看部分<一个href="#sec2">2</一个>)。此外,我们目前的攻击策略的总模拟时间民国RB 4网络(插入图)作为一个例子,作为产品的函数<我>N</我>×<我>E</我>。我们发现了一个很好的线性关系<我>t</我><sub>IB</sub>和<我>t</我><sub>理查德·道金斯</sub>和<我>N</我>×<我>E</我>对所有网络正如预期的那样,和民国高出两个数量级<我>t</我><sub>IB</sub>和<我>t</我><sub>理查德·道金斯</sub>网络等<我>N</我>×<我>E</我>。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-ff3bf644d60455be4a892601419fee4a"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.001.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-ff3bf644d60455be4a892601419fee4a partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-ff3bf644d60455be4a892601419fee4a partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 计算时间的一个完整的蒙特卡罗模拟网络节点攻击所有研究现实世界的社交网络(使用最初的中间性(IB)和重新计算程度(RD)攻击策略)和4网络(使用重新计算中间状态的策略(RB))作为产品的函数<我>N</我>×<我>E</我>(节点数(<我>N</我>)边数(<我>E</我>)。我们发现tIB, tRD规模近似线性的产品<我>N</我>×<我>E</我>,而交通研究线性扩展的产品<我>N</我> <sup>2</sup>×<我>E</我>(插入图)。从这个结果我们可以估计,RB仿真时间最大的网络数据集需要50多天使用相同的硬件。</d我v> </div> </div> </div> <p>仿真时间可以为社交网络的情况下成为一个问题,因为他们的规模非常大。事实上,据我们所知,大多数的研究动态过程在社交网络上,使用一个RB攻击策略只考虑小型少于100000节点的真实社交网络(<一个href="#B7">7</一个>,<一个href="#B28">28</一个>,<一个href="#B30">30.</一个>]。对于非常大的社交网络,RB节点攻击策略可以采取一个不切实际的时间。因此,RB不适合大型社交网络平均电脑站。另一种可能性是使用betweenness-based攻击策略只有一个中间状态的计算,即最初的中间性攻击策略IB,连同其他重新计算策略使用另一个节点的中心度规,计算代价高昂。结果,在这工作,我们考虑两个候选人攻击策略打破大真实的社交网络,IB和RD攻击策略。除了比较研究不同网络节点之间的攻击策略,其他作品关注网络鲁棒性和网络结构指标之间的关系(NSIs)。艾耶et al。<一个href="#B4">4</一个>]研究了网络的鲁棒性作为节点聚类系数的函数(或节点传递性)。研究模型与可调网络聚类系数表明,较高的网络聚类系数更强劲,与节点的最重要的影响程度和节点介数攻击(<一个href="#B4">4</一个>]。阮和董里<一个href="#B34">34</一个>]研究Facebook社交网络和发现那些网络与更高的模块化<我>问</我>删除节点的鲁棒性较低。模块性指标<我>问</我>介绍了纽曼和Girvan [<一个href="#B35">35</一个>措施如何向社区网络优惠,(即。,一个community or module in a network is a well-connected group of nodes that have sparser connections with nodes outside the group). In [<一个href="#B29">29日</一个>],作者实证分析的模块化无标度模型和现实世界的社交网络影响他们的鲁棒性和不同的节点的相对有效性攻击策略。上述研究分析网络鲁棒性和单一NSI之间的关系。</p> <p>另一方面,机器学习(ML)是一种技术,在过去的十年中,一个巨大的突破打最先进的结果在许多预测应用程序(<一个href="#B36">36</一个>]。它最初解决技术问题在计算机视觉和自然语言处理<一个href="#B37">37</一个>- - - - - -<一个href="#B39">39</一个>),然后扩展到许多其他领域,如医疗、金融、制造、能源、和环境。毫升模型的关键特征是能够智能地学习输入和输出之间的非线性关系没有明确知道他们。</p> <p>在这工作,因为这样的网络鲁棒性和NSIs之间的复杂关系,我们采用机器学习的方法来学习这样的复杂性。我们的主要贡献是毫升的应用模型来预测真实社交网络的鲁棒性和可接受的错误。我们开发毫升模型来预测网络鲁棒性两个主要攻击策略下,IB和RD攻击策略,独立。我们还实现了三种流行的ML模型、变量线性回归,multiple-variable线性回归和随机森林模型。毫升等我们的结果表明,一个数据驱动的方法可以是一个有效的方法来研究网络的复杂性。</p> <p>我们的工作包括三个步骤:(1)收集一个真实网络数据集和计算NSIs;(2)运行蒙特卡罗节点攻击模拟估计网络的鲁棒性;(3)构建和评估模型,从他们的NSIs预测网络的鲁棒性。本文的组织结构如下:在部分<一个href="#sec2">2</一个>,我们描述数据集的48个现实世界的社交网络。节<一个href="#sec3">3</一个>,我们描述了网络的健壮性蒙特卡罗模拟方法和三个毫升模型预测网络的鲁棒性,即。、简单、多元线性回归(分别单反和高钙)和随机森林(RF)模型。部分<一个href="#sec4">4</一个>介绍了主要结果,最后,我们将讨论和结论部分<一个href="#sec5">5</一个>。</p> <h4 id="real-world-social-network-datasets-and-robustness-estimation">2。现实世界的社交网络数据集和鲁棒性估计</h4> <p>真实社交网络下载来自两个来源:斯坦福大型网络数据集收集(<一个href="https://snap.stanford.edu/data/" target="_blank">https://snap.stanford.edu/data/</一个>社交网络)和网络存储库(<一个href="https://networkrepository.com/soc.php" target="_blank">https://networkrepository.com/soc.php</一个>)。我们选择48社交网络的节点数(N)等五个数量级。最小的网络是“抽动user-user网络流在葡萄牙的玩家”<我>N</我>= 1914,最大的网络“电子邮件网络从欧盟研究机构”<我>N</我>= 265216。然而,网络最大的边数(<我>E</我>)是“BlogCatalog社会博客”<我>E</我>= 4186390。在这项研究中使用的社交网络是未加权(即。,we do not take into account edge weights) and undirected (we do not consider edge directionality).</p> <p>表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab1/" target="_blank">1</一个>总结了48个真实的社交网络和他们的NSIs。除了N和<我>E</我>我们也计算以下NSIs:<span class="list"><span class="list-item"><span class="list-label">(我)</span><span class="list-content">网络密度<<我>k</我>>平均节点度,即。,the average number of edges per node.</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">安装scaled-free指数(<我>α</我>):我们假设所有社交网络度分布遵循幂律<我>P</我>(<我>k</我>)∼<我>k</我>−<我>α</我>在哪里<我>k</我>节点度。力量指数的值<我>α</我>使用普通最小平方方法安装。从这个配件,我们也提取拟合的方差<我>α</我>,用<我>α</我><sup>2</sup>。</span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">Assortativity (<我>一个</我>):assortativity系数程度之间的皮尔逊相关系数对链接节点(<一个href="#B40">40</一个>),这在−1和1之间变化。正值表示优先连接节点之间的相似度,而负值表明节点连接不同程度有更多的变化。</span></span><span class="list-item"><span class="list-label">(iv)</span><span class="list-content">模块化(<我>问</我>):模块化指标<我>问</我>计算如何划分子网的网络模块(或社区):<span class="equation_break" id="EEq1"><span class="left_break" id="L1"></span><span class="middle_break"><span class="center_break" id="M1"> <svg height="37.86pt" id="M1-1" version="1.1" viewbox="0 0 173.624 37.86" width="173.624pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B1-1"> <g transform="matrix(.013,0,0,-0.013,0,20.378)"> <path d="M699 368C699 549 574 666 407 666C186 666 23 488 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xlink:href="#g113-100"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,158.24,23.51)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,162.66,20.378)"> <path d="M364 271V272C364 550 278 798 87 953L65 927C205 795 285 542 285 271S204 -253 65 -385L87 -411C278 -259 364 -10 364 271Z" id="g119-134"></path> </g> <g transform="matrix(.013,0,0,-0.013,170.66,20.378)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="37.86pt" id="I1" version="1.1" viewbox="0 0 173.63 37.86" width="173.63pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B1-1"></use> </svg></span></span><span class="right_break" id="R1"> <svg class="label" height="11.44pt" id="M1-2" version="1.1" viewbox="0 0 13.398 11.44" width="13.398pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B1-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 611 70 451 70 272V271C70 90 136 -71 282 -169L300 -147Z" id="g190-41"></path> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M311 0V25C221 32 216 41 216 113V635C162 613 103 594 39 583V559L88 556C131 552 135 546 135 500V113C135 41 131 32 40 25V0H311Z" id="g190-213"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.9,9.26)"> <path d="M275 271C275 451 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 269V271Z" id="g190-42"></path> </g> </g> </svg> <svg class="alt_label" height="37.86pt" id="IL1" version="1.1" viewbox="0 0 13.44 37.86" width="13.44pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 13)" xlink:href="#B1-2"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里<我>E</我>边的数量,<我>一个</我><sub><i>ij</我></sub>邻接矩阵的元素是一个行吗<我>我</我>和列<我>j</我>,<我>k</我><sub><i>我</我></sub>的程度<我>我</我>,<我>k</我><sub><i>j</我></sub>的程度<我>j</我>,<我>c</我><sub><i>我</我></sub>模块(或社区)吗<我>我</我>,<我>c</我><sub><i>j</我></sub>的<我>j</我>,走过去<我>我</我>和<我>j</我>双节点,<我>δ</我>(<我>x</我>,<我>y</我>1)如果<我>x</我>=<我>y</我>否则和0 (<一个href="#B13">13</一个>]。</span></span><span class="list-item"><span class="list-label">(v)</span><span class="list-content">全局聚类系数(<我>C</我>):全球聚类系数(<我>C</我>)是基于节点的三胞胎。三联体是三个节点所连接的两个(开放三联体)或3(封闭的三联体)无向边。全局聚类系数是封闭的三胞胎的数量(或3<我>x</我>三角形,因为三角形由三个重叠的三胞胎,每个集中在三个节点)里的一个三胞胎的总数(开启和关闭)。公式如下:<span class="equation_break" id="EEq2"><span class="left_break" id="L2"></span><span class="middle_break"><span class="center_break" id="M2"> <svg height="30.6206pt" id="M2-1" version="1.1" viewbox="0 0 62.354 30.6206" width="62.354pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B2-1"> <g transform="matrix(.013,0,0,-0.013,0,18.122)"> <path 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349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,38.51,12.42)"> <path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g190-109"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,40.81,12.42)"> <path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g190-112"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,45.45,12.42)"> <path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g190-116"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,48.86,12.42)"> <path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,52.77,12.42)"> <path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path> </g> <rect height="0.65243" width="31.2422" x="26.95" y="14.469"></rect> <g transform="matrix(.013,0,0,-0.013,30.18,27.348)"> <use xlink:href="#g113-233"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.94,30.479)"> <path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z" id="g190-117"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,40.66,30.479)"> <use xlink:href="#g190-112"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.2,30.479)"> <use xlink:href="#g190-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.03,30.479)"> <path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g190-98"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,52.07,30.479)"> <use xlink:href="#g190-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.39,18.122)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R2"> <svg class="label" height="11.44pt" id="M2-2" version="1.1" viewbox="0 0 15.038 11.44" width="15.038pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B2-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M411 139C381 76 368 73 314 73H129L267 224C351 317 400 380 400 469C400 574 322 635 233 635C176 635 128 610 98 576L40 495L63 476C89 515 130 568 198 568C274 568 316 519 316 436C316 347 251 264 191 192C142 134 85 76 30 21V0H403C415 45 425 89 438 131L411 139Z" id="g190-243"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里<我>λ</我><sub>关闭</sub>是三胞胎和关闭的数量吗<我>λ</我>总在网络三胞胎的总数。全球网络聚类系数代表了总体概率相邻节点相互连接,从而使更紧密相连的模块(<一个href="#B41">41</一个>]。</span></span><span class="list-item"><span class="list-label">(vi)</span><span class="list-content">平均亲密(Cl)是所有网络节点的平均的亲密,亲密(或亲密中心)的计算节点的倒数之间的最短路径长度之和的节点和其他节点图(<一个href="#B42">42</一个>,<一个href="#B43">43</一个>]:<span class="equation_break" id="EEq3"><span class="left_break" id="L3"></span><span class="middle_break"><span class="center_break" id="M3"> <svg height="37.5951pt" id="M3-1" version="1.1" viewbox="0 0 141.218 37.5951" width="141.218pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B3-1"> <g 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336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path> </g> <g transform="matrix(.013,0,0,-0.013,63.42,31.732)"> <path d="M311 271V272C311 491 237 686 73 808L53 783C169 680 236 483 236 271C236 60 168 -138 53 -241L73 -266C237 -146 311 50 311 271Z" id="g119-6"></path> </g> <g transform="matrix(.013,0,0,-0.013,69.71,22.233)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="78.5622pt" id="I3" version="1.1" viewbox="0 0 141.95 78.5622" width="141.95pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B3-1"></use> <use transform="matrix(1 0 0 1 15.86 40.97)" xlink:href="#B3-2"></use> </svg></span></span><span class="right_break" id="R3"> <svg class="label" height="11.44pt" id="M3-3" version="1.1" viewbox="0 0 14.868 11.44" width="14.868pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B3-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M269 381C298 400 325 421 340 436C360 455 370 476 370 504C370 579 313 635 223 635H222C170 635 123 610 95 579L52 516L72 497C95 533 136 577 193 577C245 577 286 546 286 482C286 408 218 369 127 339L133 314C149 319 174 325 197 325C254 325 324 285 324 192C325 83 266 39 201 39C143 39 103 68 78 91C70 98 62 97 54 91C45 84 33 71 32 58C30 46 34 35 48 22C61 10 102 -12 148 -12C216 -12 410 57 410 225C410 298 357 362 269 379V381Z" id="g190-232"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.37,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="78.5622pt" id="IL3" version="1.1" viewbox="0 0 14.93 78.5622" width="14.93pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 33.35)" xlink:href="#B3-3"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里<我>N</我>节点和数量吗<我>d</我>(<我>我</我>,<我>j</我>)是节点之间的最短路径的长度<我>我</我>和<我>j</我>。</span></span></span></p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 结构统计数据现实世界的社交网络:节点(<我>N</我>),边缘(<我>E</我>),平均节点度<<我>k</我>>,符合幂律指数<我>α</我>拟合方差的幂律指数<我>α</我> <sup>2</sup>,assortativity系数<我>一个</我>、模块化<我>问</我>、全局聚类系数<我>C</我>亲密,平均节点<我>Cl</我>。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2022/3616163/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <h5 id="sec2.1">2.1。网络鲁棒性蒙特卡罗模拟</h5> <p>对于每个网络,我们使用蒙特卡罗模拟运行两个节点删除过程。节点连续中移除后最初的中间性的排名(IB)和重新计算程度的排名(RD)。的关系,例如,节点与平等的中间性或程度得分,我们随机删除其中的一个。每个节点删除后,我们计算网络健壮性测量和相对大小最大的连接组件LCC,一起积累比例的节点删除<我>问</我>。最后,我们获得两条曲线LCC (<我>问</我>)对应于两个节点删除流程,IB和RD。整个模拟重复10次,最后曲线LCC (<我>问</我>)的平均结果。</p> <p>此外,我们计算一个值定义为网络的鲁棒性(<我>R</我>),由Bellingeri et al。<一个href="#B44">44</一个>),而规范化的LCC曲线下面的面积在清除过程中,<我>R</我>=<span class="nowrap"> <svg height="15.9799pt" id="M4" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -12.5505 39.8983 15.9799" width="39.8983pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="39.7987" x="0" y="-11.8482"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z" id="g190-77"></path> </g> <g transform="matrix(.013,0,0,-0.013,6.89,0)"> <path d="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z" id="g190-68"></path> </g> <g transform="matrix(.013,0,0,-0.013,15.626,0)"> <use xlink:href="#g190-68"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.362,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> </g> <g transform="matrix(.013,0,0,-0.013,28.86,0)"> <path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z" id="g113-114"></path> </g> <g transform="matrix(.013,0,0,-0.013,35.243,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> </g> </svg>。</span><i>R</我>因此可以两个理论之间的极端,<span class="inline_break"> <svg height="8.8423pt" id="M5" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 19.414 8.8423" width="19.414pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.783,0)"> <path d="M535 138V188H52V138H535ZM536 353L507 390C486 357 454 333 416 333C388 333 343 353 308 370C264 391 211 414 171 414C121 414 78 382 49 340L80 307C100 339 133 364 171 364C197 364 244 343 279 326C323 305 374 283 416 283C465 283 506 314 536 353Z" id="g117-134"></path> </g> </svg><span class="irelop"></span> <svg height="8.8423pt" style="vertical-align:-0.2064009pt" version="1.1" viewbox="22.9961838 -8.6359 6.422 8.8423" width="6.422pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,23.046,0)"> <path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path> </g> </svg></span>(绝对脆弱的网络)<span class="inline_break"> <svg height="8.8423pt" id="M6" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 19.414 8.8423" width="19.414pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.783,0)"> <use xlink:href="#g117-134"></use> </g> </svg><span class="irelop"></span> <svg height="8.8423pt" style="vertical-align:-0.2064009pt" version="1.1" viewbox="22.9961838 -8.6359 15.66 8.8423" width="15.66pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,23.046,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.286,0)"> <path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path> </g> <g transform="matrix(.013,0,0,-0.013,32.25,0)"> <path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path> </g> </svg></span>(绝对强大的网络)。我们表示RRD和肋骨网络鲁棒性对RD和IB节点攻击策略,分别。</p> <p>总之,我们收集48个真实的社交网络,然后我们计算9 NSIs为每个网络作为输入。同时,我们运行蒙特卡罗模拟和获取两个指标所代表的鲁棒性,RRD和肋骨。越高,网络更健壮。这两个指标是每个网络的输出和将使用毫升预测模型。</p> <h4 id="machine-learning-approach">3所示。机器学习方法</h4> <p>本节介绍了单反的细节,高钙,射频模型。</p> <h5 id="sec3.1">3.1。简单线性回归模型(SLR)</h5> <p>线性回归是最简单的预测模型。网络之间的单反相机模型的鲁棒性<我>R</我>和一个NSI<我>x</我>由线性方程表示:<span class="equation_break" id="EEq4"><span class="left_break" id="L7"></span><span class="middle_break"><span class="center_break" id="M7"> <svg height="13.8661pt" id="M7-1" version="1.1" viewbox="0 0 68.594 13.8661" width="68.594pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B7-1"> <g transform="matrix(.013,0,0,-0.013,0,9.184)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.78,9.184)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.04,9.184)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,29.04,12.316)"> <path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path> </g> <g transform="matrix(.013,0,0,-0.013,36.89,9.184)"> <path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path> </g> <g transform="matrix(.013,0,0,-0.013,47.43,9.184)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.42,12.316)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.36,9.184)"> <path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path> </g> <g transform="matrix(.013,0,0,-0.013,65.63,9.184)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R7"> <svg class="label" height="11.44pt" id="M7-2" version="1.1" viewbox="0 0 15.458 11.44" width="15.458pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B7-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M465 179V225H369V632H330C227 497 124 346 29 205V179H289V107C289 37 284 33 198 26V0H454V26C374 33 369 37 369 107V179H465ZM289 225H92C156 335 222 430 287 520H289V225Z" id="g190-166"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.96,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<我>一个</我><sub>0</sub>是拦截和<我>一个</我><sub>1</sub>斜率是。在(<一个href="#EEq4">4</一个>),一个普通的最小二乘法(OLS)申请估计系数通过最小化一个适当的损失函数(<一个href="#B45">45</一个>,<一个href="#B46">46</一个>]。一旦OLS的过程,也称拟合过程,被执行时,我们可以使用(1)预测的鲁棒性<我>R</我>一个新的网络对于一个给定的指标<我>x</我>。此外,我们得出一个统计数据<我>t</我>以及从零假设H0的OLS过程:<我>一个</我><sub>1</sub>= 0。拒绝H0意味着之间存在显著的线性关系<我>R</我>和NSI<我>x</我>。</p> <p>我们运行单反模型适合所有NSIs列在表中<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab1/" target="_blank">1</一个>不包括<我>E</我>因为它可以表达的另外两个NSIs:<我>E</我>=<我>N</我><<我>k</我>> / 2。</p> <h5 id="sec3.2">3.2。多元线性回归模型</h5> <p>看不到多元线性回归(MLR)是一个扩展的单反多维变量<我>x</我>= (<我>x</我><sub>1</sub>,<我>x</我><sub>2</sub>、…<我>x</我><sub><i>n</我></sub>),<我>x</我><sub>1</sub>,<我>x</我><sub>2</sub>、…<我>x</我><sub><i>n</我></sub>NSIs。网络鲁棒性之间的线性方程<我>R</我>和NSIs如下:<span class="equation_break" id="EEq5"><span class="left_break" id="L8"></span><span class="middle_break"><span class="center_break" id="M8"> <svg height="13.8661pt" id="M8-1" version="1.1" viewbox="0 0 173.724 13.8661" width="173.724pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B8-1"> <g transform="matrix(.013,0,0,-0.013,0,9.184)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.79,9.184)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.05,9.184)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,29.04,12.316)"> <use 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</svg></span></span>在哪里<我>一个</我><sub><i>我</我></sub>系数从OLS方法获得。</p> <h5 id="sec3.3">3.3。随机森林模型</h5> <p>随机森林(RF)属于毫升模型的集合类,表明它总量预测的合奏毫升基础模型,在这里,决策树回归(DTR)模型。我们简要描述DTR在接下来的部分。</p> <p>DTR开始与树的根包含所有样品(48网络在我们的例子中)。然后它分裂成两个不同的节点通过选择样本的某个变量的值高于或低于某一阈值。图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig2/" target="_blank">2(一个)</一个>代表一个数据集的基本决策树图。根节点包含48网络分裂成两个其他节点通过考虑是否变量(NSI)在我们的例子中无标度指数<我>α</我>高于或低于2.5。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-48d51be98f7ff215d3e9c3238e2bec3f"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.002a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.002b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-48d51be98f7ff215d3e9c3238e2bec3f partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.002a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.002b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-48d51be98f7ff215d3e9c3238e2bec3f partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> (一)决策树的一个例子:根节点包含48网络分裂成两个其他节点,节点11和节点12、13和35网络,分别根据无标度指数的值<我>α</我>。节点12分裂成两个其他节点,节点和节点21日22日与15和20网络,分别根据网络密度的值<<我>k</我>>。我们假设在节点11,21岁的节点和节点22日不可能分裂,因为某些停止规则,因此,他们成为最后的叶子。一般来说,可以使用任何NSI划分网络在任何分裂,和决策树可以根据停止任意复杂的规则。(b)的说明进行相同的决策树(<我>α</我>和<<我>k</我>>)空间最后的叶子。</d我v> </div> </div> </div> <p>DTR选择变量,其分裂值是基于信息理论,具体考虑熵的概念。熵是一个度量不确定性的一个节点。DTR分裂节点通过最大化信息增益,即加权区别两个结果节点的总熵和熵的初始节点。DTR先后分裂,直到达到停止条件,例如,如果当前节点的大小小于20。最后的节点也被称为一个叶子节点。在图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig2/" target="_blank">2(一个)</一个>第一次分裂后,根,左子节点成为一个叶节点,而右子节点继续分裂成两个叶节点。</p> <p>一旦最终DTR,它可以用来预测新样本的值如下。新样品将分为一个叶子,和其预测价值将所有样本的平均值,分为相同的叶子。</p> <p>最后,RF模型创建多个决策树的随机数据,通常几百,平均结果从所有树木输出一个新的结果常常会导致强烈的预测(<一个href="#B47">47</一个>,<一个href="#B48">48</一个>]。</p> <p>决策树可以适合非线性的数据集,因为它可以把同样的NSI很多次了。然而,决策树是容易过度拟合,即。,我t我s too sensitive to the training data while failing to predict new coming (testing) data. In order to address this problem, a random forest (RF) model is obtained by creating multiple randomly drawn decision trees from data, usually several hundred. The final regression prediction will be the average prediction of all the decision trees [<一个href="#B47">47</一个>- - - - - -<一个href="#B49">49</一个>)(在这项工作中,我们实现一个射频300 dtr)。使用射频,”功能重要性”等级的测量可以派生NSI [<一个href="#B50">50</一个>]。</p> <h5 id="sec3.4">3.4。数据准备、验证和绩效评估</h5> <p>所有NSIs可以从网络计算的数据,因此,我们的数据集不包含缺失值。我们也排除<我>E</我>正如上面提到的,因为冗余。其他8 NSIs规范化,避免巨大差异指标的范围:<span class="equation_break" id="EEq6"><span class="left_break" id="L9"></span><span class="middle_break"><span class="center_break" id="M9"> <svg height="18.6667pt" id="M9-1" version="1.1" viewbox="0 0 120.184 18.6667" width="120.184pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B9-1"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.27,6.222)"> <path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.21,16.269)"> <use 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</svg></span></span>在哪里<svg height="11.4899pt" id="M10" style="vertical-align:-5.52899pt" version="1.1" viewbox="-0.0498162 -5.96091 16.4767 11.4899" width="16.4767pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.75,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.907,3.132)"> <use xlink:href="#g50-107"></use> </g> </svg>NSI的价值吗<我>我</我>观察(网络)<我>j</我>和<svg height="12.5142pt" id="M11" style="vertical-align:-3.291141pt" version="1.1" viewbox="-0.0498162 -9.22306 10.4495 12.5142" width="10.4495pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="7.29424" x="0" y="-8.52081"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.294,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>和<svg height="12.5794pt" id="M12" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 26.7866 12.5794" width="26.7866pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.347,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.845,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.047,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.103,0)"> <use xlink:href="#g113-42"></use> </g> </svg>的均值和标准差NSI吗<我>我</我>,分别。</p> <p>在第一步中,我们使用整个数据集构建毫升模型和模型之间的比较结果和两个目标变量。然而,由于许多毫升模型过度拟合问题,新数据模型的性能并不总是一致的,在训练的步骤中,我们需要在第二步验证模型。我们选择的分析验证<一个href="#B51">51</一个>]。通过这种方式,我们训练的每个模型48次以上:每一次整个数据集包括一个观察是用来训练模型,然后,该模型用于预测的目标价值剩余的(合作)观察和重复每48个同意的观察。综合评价结果的平均所有48回归。</p> <p>指出,单反的模型中,我们只考虑回归系数来分析鲁棒性指标对每个NSI的依赖。然而,对于高钙和射频模型,我们使用四种常见分析鲁棒性指标的预测评价指标回归问题,均方根误差(RMSE)和确定系数(也叫解释方差比,<我>R</我><sup>2</sup>)为分析指标和频率分布和残余的qq阴谋错误图形指标。</p> <p>RMSE是根号的平方的总和观察和预测数据点之间的区别。RMSE有相同的单位作为目标特性和模型通常被认为是错误。较低的权值代表优越的预测结果。RMSE提供的公式<span class="equation_break" id="EEq7"><span class="left_break" id="L13"></span><span class="middle_break"><span class="center_break" id="M13"> <svg height="45.4571pt" id="M13-1" version="1.1" viewbox="0 0 34.578 45.4571" width="34.578pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B13-1"> <g transform="matrix(.013,0,0,-0.013,0,33.095)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.15,33.095)"> <path d="M962 650H795L470 145L347 650H176L170 622C268 613 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xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,130.63,21.353)"> <use xlink:href="#g119-134"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,136.5,12.16)"> <use xlink:href="#g50-51"></use> </g> <rect height="0.65243" width="118.202" x="23.25" y="29.441"></rect> <g transform="matrix(.013,0,0,-0.013,79.07,42.321)"> <path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path> </g> <g transform="matrix(.013,0,0,-0.013,142.65,33.095)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R13"> <svg class="label" height="11.44pt" id="M13-3" 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</svg></span></span>在哪里<我>n</我>是观察,的数量<我>R</我><sub><i>j</我></sub>是模拟的鲁棒性,<我>R</我><sub>预测,<我>j</我></sub>表示观测的预测值<我>j</我>,<svg height="17.427pt" id="M15" style="vertical-align:-5.5289pt" version="1.1" viewbox="-0.0498162 -11.8981 12.707 17.427" width="12.707pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="8.18155" x="0" y="-11.1958"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.182,3.132)"> <use xlink:href="#g50-107"></use> </g> </svg>是平均的仿真的鲁棒性。<我>R</我><sup>2</sup>0之间的不同(模型没有预测能力)和1(模型正确预测所有的值)。</p> <p>剩余误差,<span class="inline_break"> <svg height="14.0004pt" id="M16" style="vertical-align:-5.3645pt" version="1.1" viewbox="-0.0498162 -8.6359 16.594 14.0004" width="16.594pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M387 375C387 402 357 448 257 448C172 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transform="matrix(.0091,0,0,-0.0091,107.787,3.132)"> <use xlink:href="#g190-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.508,3.132)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,114.421,3.132)"> <use xlink:href="#g190-101"></use> </g> </svg>,</span></span>只是一个错误之间的经验(模拟)的预测价值网络的鲁棒性和鲁棒性。的分布直方图<svg height="6.1673pt" id="M17" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.44961 6.1673" width="5.44961pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-247"></use> </g> </svg>预计将接近原点。此外,最重要的一个线性回归模型的假设是残余错误是独立的,因此,这些错误将正态分布。</p> <p>分析了网络使用的“制图工具”图书馆<我>Python</我>。所有数据准备、模型建立和评价是用写的<我>Python</我>代码。数值模拟是一个PC的硬件以19 - 10850英特尔处理器和32 GB RAM。</p> <h4 id="results">4所示。结果</h4> <h5 id="sec4.1">4.1。网络鲁棒性的函数NSIs和单反t检验</h5> <p>每个网络的鲁棒性仿真肋骨和RRD表表示<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab2/" target="_blank">2</一个>。总的来说,我们发现RRD略小于肋对大多数网络(43 48网络),平均分别为0.148和0.173。它表明RD策略更有功效比IB攻击现实世界的社交网络。最大的和稀疏网络,Email-EuAll (<我>N</我>= 265216和<<我>k</我>≥1.58),具有最小的鲁棒性与一个平等的肋骨和RRD 0.001。相比之下,gemsec_deezer_HR网络<我>N</我>= 54575和<<我>k</我>≥9.12,具有最强的鲁棒性的肋骨和RRD 0.375和0.338,分别。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 仿真结果通过IB和RD节点攻击策略,由网络鲁棒性指标<我>R</我> <sub>IB</sub>和<我>R</我> <sub>理查德·道金斯</sub>,所有48个现实世界的社交网络(网络的尺寸从最小到最大)。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2022/3616163/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <p>在图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig3/" target="_blank">3</一个>,我们把RRD和肋骨8独立NSIs的函数,我们发现RRD和肋骨的行为同样在所有情况下。单反揭示一些重要的之间的关系<我>R</我>和NSIs(图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig3/" target="_blank">3</一个>和表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab3/" target="_blank">3</一个>)。例如,在图3(一个),我们可以看到,RRD和肋骨稍微减少网络的大小<我>N</我>。这个线性鲁棒性RRD和肋骨之间的依赖<我>N</我>测试通过使用单反相机模型,我们发现它是统计学意义,置信水平为95% (<svg height="10.2124pt" id="M18" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path> </g> </svg>值< 0.05,表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab3/" target="_blank">3</一个>)。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-b11293d54e199e6352507a7db30919de"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003b.jpg"> <br> <strong>(b)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003c.jpg"> <br> <strong>(c)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003d.jpg"> <br> <strong>(d)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(e)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003e.jpg"> <br> <strong>(e)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(f)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003f.jpg"> <br> <strong>(f)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(g)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003g.jpg"> <br> <strong>(g)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(h)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.003h.jpg"> <br> <strong>(h)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-b11293d54e199e6352507a7db30919de partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003b_th.jpg"><br><strong>(b)</strong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003c_th.jpg"><br><strong>(c)</strong></button> <button aria-label="Slide to (d) " class="partial-carousel-dot"><img loading="lazy" alt="(d)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003d_th.jpg"><br><strong>(d)</strong></button> <button aria-label="Slide to (e) " class="partial-carousel-dot"><img loading="lazy" alt="(e)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003e_th.jpg"><br><strong>(e)</strong></button> <button aria-label="Slide to (f) " class="partial-carousel-dot"><img loading="lazy" alt="(f)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003f_th.jpg"><br><strong>(f)</strong></button> <button aria-label="Slide to (g) " class="partial-carousel-dot"><img loading="lazy" alt="(g)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003g_th.jpg"><br><strong>(g)</strong></button> <button aria-label="Slide to (h) " class="partial-carousel-dot"><img loading="lazy" alt="(h)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.003h_th.jpg"><br><strong>(h)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-b11293d54e199e6352507a7db30919de partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 仿真结果通过IB和RD节点攻击策略,由网络鲁棒性指标<我>R</我> <sub>IB</sub>和<我>R</我> <sub>理查德·道金斯</sub>,所有的48现实世界的社交网络作为8 NSIs的函数。</d我v> </div> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 8 NSIs的单反效果。最后两列显示斜率,在括号,<我>R</我> <sup>2</sup>之间的单反NSI值和肋骨或RRD。大胆的性格和星号表示重要的关系,与95%的置信水平。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2022/3616163/tab3" target="_blank" aria-label="View full page"></a> </div> </div> <p>有趣的是,RRD和肋骨不统计线性依赖于网络密度<<我>k</我>>,发现以前在<一个href="#B4">4</一个>,<一个href="#B52">52</一个>)(图3 (b)和表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab3/" target="_blank">3</一个>)。这种对比观察表明,网络健壮性还取决于其他NSIs和网络密度无法预测以往整个网络的鲁棒性。</p> <p>除了<我>N</我>唯一的其他NSI显示显著的线性关系是模块化<我>问</我>(图3 (f))在RRD的情况下。</p> <p>然而,在图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig3/" target="_blank">3</一个>,我们还观察到一些非线性依赖关系。例如,在图3 (e),我们表明,网络健壮性随assortativity系数时<我>一个</我>> 0。然而,它也减少了更快的时候<我>一个</我>接近0时,增加<我>一个</我>< 0。</p> <p>同样,在图3中(g),我们发现RRD和肋骨之间的关系和全球聚类系数C遵循一个倒u形的模式。我们运行了一个两行统计检验(<一个href="#B53">53</一个>),发现两行(或折线)回归明显比一个单行的测试。断点被发现<我>C</我>= 0.115。RRD和肋骨线性增加C(显著性水平为95%)断点和线性减少与C(显著性水平为95%)。一个可能的解释是,如果网络稀疏,更多的三胞胎帮助增加网络的连通性,从而提高其鲁棒性。然而,超过一定值(当<我>C</我>= 0.115),更多的三胞胎可能表示中心或中心节点的存在,这很可能是故意的目标节点删除RD和IB等策略,从而降低网络的鲁棒性。</p> <h5 id="sec4.2">4.2。机器学习的预测网络的鲁棒性</h5> <p>前一节的结果表明,社交网络的鲁棒性取决于多个NSIs高度复杂,多维、非线性的方式。提高模型预测,在这一节中,我们使用两个多个变量毫升模型,高钙和射频,预测网络的鲁棒性。</p> <p>多元线性回归的结果高如表所示<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab4/" target="_blank">4</一个>。我们发现两个<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>有一个积极的整体线性回归系数对吗<我>α</我>,<我>问</我>,<我>Cl</我>,<<我>k</我>>和负总体线性回归系数有关<我>α</我><sup>2</sup>,<我>一个</我>,<我>C</我>,<我>N</我>。此外,高钙的结果表明<我>α</我>,<我>α</我><sup>2</sup>,<<我>k</我>>是最显著的系数。一个积极的线性回归系数的平均节点度<<我>k</我>>时表明,网络更健壮<我>k</我>是较高的,而所有其他NSIs是固定的。这个结果同意先前的结果证明密集的网络可能抗攻击(<一个href="#B4">4</一个>,<一个href="#B52">52</一个>]。然而,高钙之间的不同的结果和单反建议<之间有很强的相关性<我>k</我>>和其他NSIs。此外,高钙模型预测<我>R</我><sub>IB</sub>比<我>R</我><sub>理查德·道金斯</sub>,<我>R</我><sup>2</sup>系数58.04%到51.76%。然而,RMSE小<我>R</我><sub>理查德·道金斯</sub>值为0.0657,相比0.0709肋(这是因为肋骨的标准差比高<我>R</我><sub>理查德·道金斯</sub>,如表所示<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab2/" target="_blank">2</一个>(底下一行))。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 适应系数的评价结果高。<我>R</我> <sub>IB</sub>或<我>R</我> <sub>理查德·道金斯</sub>列显示斜率系数,在括号,标准误差的NSI值。大胆的性格和星号表示重要的NSI和鲁棒性之间的关系<我>R</我>,在95%的置信水平。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2022/3616163/tab4" target="_blank" aria-label="View full page"></a> </div> </div> <p>由于非线性的发现在前面的小节中,我们预计使用射频模型回归结果将得到改善。表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab5/" target="_blank">5</一个>代表了射频模型的回归结果。我们发现<我>R</我><sup>2</sup>增加到92.24%和91.88%<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>分别回归。有趣的是,RF模型预测<我>R</我><sub>理查德·道金斯</sub>大致一样<我>R</我><sub>理查德·道金斯</sub>,而高预测<我>R</我><sub>IB</sub>比<我>R</我><sub>理查德·道金斯</sub>,这表明<我>R</我><sub>理查德·道金斯</sub>可能比肋与NSIs遵循一个更强的非线性关系。此外,RMSE改进的<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>,其值分别为0.0272和0.0241。有趣的是,该功能重要性排名在表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab5/" target="_blank">5</一个>与一个射频模型表明,assortativity,全球亲密<我>C</我>和节点数量<我>N</我>NSIs是最重要。这个结果同意探索观察如图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig3/" target="_blank">3</一个>正如上面所讨论的。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab5"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表5</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/tab5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 功能的重要性NSI和射频的评价结果。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2022/3616163/tab5" target="_blank" aria-label="View full page"></a> </div> </div> <p>在图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig4/" target="_blank">4</一个>,我们比较网络的鲁棒性<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>预测的值由高钙和射频使用散点图。散点图表明,射频数据明显比高,实际预测的数据点在哪里靠近对角线<我>y</我>=<我>x</我>。同时,高钙回归,我们仍然发现非线性实际值和预测值之间的依赖关系。事实上,高钙模型无法捕捉的固有非线性依赖实际数据。我们也分析了残余的上述回归错误使用频率直方图和QQ-plot,发现他们遵循正态分布相对较好(数字<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig5/" target="_blank">5</一个>- - - - - -<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig8/" target="_blank">8</一个>)。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-3d5ff74481853747b9f8840116fb8384"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.004a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.004b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-3d5ff74481853747b9f8840116fb8384 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.004a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.004b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-3d5ff74481853747b9f8840116fb8384 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 鲁棒性的预测价值之间的散点图(<我>R</我>预测和模拟<我>R</我>经验)高(a) (b)和射频模型。该模型是使用整个训练数据集,数据集和预测的值是相同的。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-298463833c9a2c26d429caa150c00d36"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.005a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.005b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-298463833c9a2c26d429caa150c00d36 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.005a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.005b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-298463833c9a2c26d429caa150c00d36 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图IB残留高预测错误的策略对整个数据集(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-52883e76209b9fe5d007f2a195cc78ed"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.006a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.006b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-52883e76209b9fe5d007f2a195cc78ed partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.006a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.006b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-52883e76209b9fe5d007f2a195cc78ed partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图RD儿童高预测残留误差的策略对整个数据集(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-8b335be350c97f905217514609193999"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.007a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.007b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-8b335be350c97f905217514609193999 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.007a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.007b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-8b335be350c97f905217514609193999 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图的残余误差对射频IB策略的预测对整个数据集(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-0c048234bea08584ecc3626b431b897e"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.008a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.008b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-0c048234bea08584ecc3626b431b897e partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.008a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.008b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-0c048234bea08584ecc3626b431b897e partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图的残余误差对射频RD策略的预测对整个数据集(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <p>最后,我们运行分析回归模型高钙和射频为了避免过度拟合。结果总结表<一个href="//www.newsama.com/journals/complexity/2022/3616163/tab6/" target="_blank">6</一个>散点图如图<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig9/" target="_blank">9</一个>。我们发现准确的预测结果是低于上述“样本”训练较低的均方根高钙和射频模型。我们得到一个RMSE的0.0812和0.0760<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>分别预测使用高钙和RMSE的0.0733和0.0636<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>分别预测使用射频。尽管回归结果不太有效,因为我们预测单一独立于其余的样品样品用于培训(构建毫升模型),剩余错误仍然适合一个正态分布直方图和QQ-plots(数据所示<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig10/" target="_blank">10</一个>- - - - - -<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig13/" target="_blank">13</一个>)。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab6"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表6</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/tab6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 高钙和射频使用分析方法评价结果。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2022/3616163/tab6" target="_blank" aria-label="View full page"></a> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-e61fc5d9f81980fe7f6f766c8df306cf"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.009a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.009b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-e61fc5d9f81980fe7f6f766c8df306cf partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.009a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.009b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-e61fc5d9f81980fe7f6f766c8df306cf partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 鲁棒性的预测价值之间的散点图(<我>R</我>预测和模拟<我>R</我>抵抗观测的经验)高(a) (b)和射频模型。该模型是使用整个训练数据集包括一个观察(抵抗观测),是用来预测的结果尚未签署的观察。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-5270244a0b2840a35d8d5fd82c0e5871"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0010a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0010b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-5270244a0b2840a35d8d5fd82c0e5871 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0010a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0010b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-5270244a0b2840a35d8d5fd82c0e5871 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图10</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图IB残留高预测错误的战略分析样本(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-4727609d248f0e18fec7baee50dc75bd"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0011a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0011b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-4727609d248f0e18fec7baee50dc75bd partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0011a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0011b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-4727609d248f0e18fec7baee50dc75bd partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图11</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图RD儿童高预测残留误差的战略分析样本(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-b812c2fbc2a3571d741200f6cfb2152d"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0012a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0012b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-b812c2fbc2a3571d741200f6cfb2152d partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0012a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0012b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-b812c2fbc2a3571d741200f6cfb2152d partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图12</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig12/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图射频预测残留误差的IB战略分析样本(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-0914867366b2f14dedd049999c667af4"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0013a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/figures/3616163.fig.0013b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-0914867366b2f14dedd049999c667af4 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0013a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2022/3616163/thumbnails/3616163.fig.0013b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-0914867366b2f14dedd049999c667af4 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图13</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2022/3616163/fig13/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 直方图的射频预测残留误差RD战略分析样本(一)及其QQ-plot (b)。</d我v> </div> </div> </div> <h4 id="discussion-and-conclusion">5。讨论和结论</h4> <p>在这项工作中,我们分析了48个现实世界的社交网络的鲁棒性和节点数量等五个数量级,从1914年到265216年。使用蒙特卡罗模拟,我们有两种常用的节点攻击策略运行,IB和RD策略,其计算时间是在我们的硬件功能。我们发现相应的仿真时间,<我>t</我><sub>IB</sub>和<我>t</我><sub>理查德·道金斯</sub>,尺度线性的产品网络的节点数和边数,也就是说,<我>N</我>×<我>E</我>。我们还发现,这两个攻击策略IB和RD独特的鲁棒性度量相似的疗效评估<我>R</我>与RD略优于IB(平均水平<我>R</我><sub>理查德·道金斯</sub>是略小于平均<我>R</我><sub>IB</sub>)。它表明,在这项研究中,使用的社交网络采访策略是最有效的策略来拆除(分解)网络,无论是计算成本和分解效率。</p> <p>了解社交网络的结构决定了其鲁棒性,我们调查指标之间的关系<我>R</我>和一组网络结构指标(NSIs)的文学。简单线性回归(SLR)之间<我>R</我>NSIs显示低善良的拟合,整体是不能够产生显著的预测模型。单反的低善将表明,网络健壮性取决于NSIs以非线性的方式。</p> <p>提高拟合,我们开发了两个机器学习模型预测两个鲁棒性指标<我>R</我><sub>理查德·道金斯</sub>和<我>R</我><sub>理查德·道金斯</sub>从8 NSIs的结合,多元线性回归(高),(RF)和随机森林模型。后者的一个选择,因为它可以处理非线性数据,是建立在基础模型的集合,决策树分类器。我们发现明显的随机森林模型可以预测网络的鲁棒性优于多元线性回归模型。在混凝土中,射频模式预测网络鲁棒性的RMSE 0.0272和0.0241<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>,分别。这个结果是令人鼓舞的预测的真实社交网络的鲁棒性,虽然错误(约16%<我>R</我><sub>IB</sub>,RMSE比平均为0.0272<我>R</我><sub>IB</sub>是0.173,<我>R</我><sub>理查德·道金斯</sub>,RMSE比平均为0.0241<我>R</我><sub>理查德·道金斯</sub>0.148)。与此同时,分析评价时,RMSE增加到0.0733和0.0636<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>分别大约三分之一的平均值。</p> <p>最后,高表明,最重要的因素来预测肋指数<我>α</我>和平均节点度<<我>k</我>>,<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>。特别是,一个更高的价值<我>α</我>与高<我>R</我><sub>IB</sub>和<我>R</我><sub>理查德·道金斯</sub>。高指数的绝对值<我>α</我>表示一个网络中心节点较少(高度连接节点)(<一个href="#B35">35</一个>]。因此,RD和IB攻击策略无法找到大型枢纽节点的删除可能瓦解网络更快,导致更高的值<我>R</我><sub>理查德·道金斯</sub>和<我>R</我><sub>IB</sub>。此外,高表明<<我>k</我>>是正相关的降低<我>R</我><sub>IB</sub>和<我>R</我><sub>IB</sub>。这最后的结果同意以前的结果,证明网络边缘密度较高的可能更耐攻击(<一个href="#B4">4</一个>,<一个href="#B52">52</一个>]。另一方面,它证实了单反,专注于单一NSI可能无法预测真实社交网络的鲁棒性。</p> <p>我们的工作表明,ML模型可以用来预测网络的鲁棒性与可接受的结果。因此,缓解需要运行一个完整的蒙特卡罗模拟网络上只有近似健壮性是必要的。与此同时,更多的网络数据集将改善毫升模型的准确性。这个工作也有助于理解现实世界的社交网络的鲁棒性之间的关系和其结构指标。最后,我们证明,使用数据驱动的方法预测的结果非线性和复杂的动态过程,如网络的鲁棒性,是一个适当的方法<一个href="#B54">54</一个>- - - - - -<一个href="#B60">60</一个>]。</p> <h4 id="appendix">附录</h4> <p>直方图和QQ-plot残余误差的回归给出了数据<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig5/" target="_blank">5</一个>- - - - - -<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig8/" target="_blank">8</一个>和数字<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig10/" target="_blank">10</一个>- - - - - -<一个href="//www.newsama.com/journals/complexity/2022/3616163/fig13/" target="_blank">13</一个>。</p> <h4 id="abbreviations">缩写</h4> <table class="gloss-abbr"> <tbody> <tr> <td>理查德·道金斯:</td> <td>重新计算度节点攻击策略</td> </tr> <tr> <td>IB:</td> <td>最初的中间性节点攻击策略</td> </tr> <tr> <td>RB:</td> <td>重新计算介数节点攻击策略</td> </tr> <tr> <td><i>t</我><sub>IB</sub>:</td> <td>IB仿真总时间攻击策略</td> </tr> <tr> <td><i>t</我><sub>理查德·道金斯</sub>:</td> <td>路仿真总时间攻击策略</td> </tr> <tr> <td><i>t</我><sub>RB</sub>:</td> <td>RB仿真总时间攻击策略</td> </tr> <tr> <td>单反:</td> <td>简单线性回归模型</td> </tr> <tr> <td>高:</td> <td>多元线性回归模型</td> </tr> <tr> <td>射频:</td> <td>随机森林模型</td> </tr> <tr> <td>DTR:</td> <td>决策树回归模型</td> </tr> <tr> <td>NSI:</td> <td>网络结构指标</td> </tr> <tr> <td>RMSE:</td> <td>均方误差</td> </tr> <tr> <td><i>R</我><sup>2</sup>:</td> <td>确定系数(也叫解释方差比率)</td> </tr> <tr> <td><i>一个</我><sub>0</sub>:</td> <td>拦截系数单反</td> </tr> <tr> <td><i>一个</我><sub>1</sub>:</td> <td>斜率系数单反</td> </tr> <tr> <td>OLS:</td> <td>普通最小二乘法</td> </tr> <tr> <td><span class="nowrap"> <svg height="6.1673pt" id="M33" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.44961 6.1673" width="5.44961pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-247"></use> </g> </svg>:</span></td> <td>误差之间的经验(模拟)的预测价值网络的鲁棒性和鲁棒性</td> </tr> <tr> <td><i>α</我>:</td> <td>安装无标度指数</td> </tr> <tr> <td><i>k</我>:</td> <td>节点度</td> </tr> <tr> <td><<我>k</我>>:</td> <td>平均节点度</td> </tr> <tr> <td><i>一个</我>:</td> <td>学位assortativity</td> </tr> <tr> <td><i>Cl</我>:</td> <td>全球亲密</td> </tr> <tr> <td><i>C</我>:</td> <td>全局聚类系数</td> </tr> <tr> <td>低成本航空:</td> <td>最大连接组件</td> </tr> <tr> <td><i>N</我>:</td> <td>的节点数量</td> </tr> <tr> <td><i>E</我>:</td> <td>边数</td> </tr> <tr> <td><i>问</我>:</td> <td>模块化的指标</td> </tr> <tr> <td><i>α</我><sup>2</sup>:</td> <td>拟合方差<我>α</我></td> </tr> <tr> <td><i>问</我>:</td> <td>积累比例的节点删除</td> </tr> <tr> <td><i>R</我>:</td> <td>网络鲁棒性</td> </tr> <tr> <td><i>R</我><sub>理查德·道金斯</sub>:</td> <td>网络鲁棒性对RD节点攻击策略</td> </tr> <tr> <td><i>R</我><sub>IB</sub>:</td> <td>网络鲁棒性对IB节点攻击策略。</td> </tr> </tbody> </table> <h4 id="data-availability">数据可用性</h4> <p>所有48个真实的社交网络从斯坦福下载大型网络数据集收集(<一个href="https://snap.stanford.edu/data/" target="_blank">https://snap.stanford.edu/data/</一个>社交网络)和网络存储库(<一个href="https://networkrepository.com/soc.php" target="_blank">https://networkrepository.com/soc.php</一个>)。</p> <h4 id="conflicts-of-interest">的利益冲突</h4> <p>作者宣称没有利益冲突。</p> <h4 id="authors’-contributions">作者的贡献</h4> <p>QN构思分析。NKKN,水马力,TTL和TMN执行模拟。QN NKKN, FS,风湿性关节炎,MB, DC写道。</p> <h4 id="acknowledgments">确认</h4> <p>这项工作是由越南科学技术部(大多数)Vietnam-Italy科技合作项目2021 - 2023年期间,越南胡志明市国立大学(VNU-HCM),越南胡志明市,在格兰特B2017-42-01号。这项研究是由意大利外交部的资助以及国际合作。这个项目获得资金从欧洲研究委员会(ERC)在欧盟的地平线2020研究和创新计划(批准的协议。(816313))。作者非常感谢范·朗大学越南,为本研究提供的预算。</p> </div> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 class="ArticleReferences_references__GH2t_" id="references">引用</h4> <ol class="ArticleReferences_orderedReferences__mJr9M"> <li class="ArticleReferences_articleReference__ouEuh" id="B1"> <div class="referenceContent"> <p class="referenceText">美国莱曼和y y。安,“复杂的传播现象在社会系统中,“<我>计算社会科学)</我>施普林格国际出版,柏林,德国,2018年。</p>视图: <a 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