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article_header_class"> <p class="sc-gmeYpB ctdkmR article_type">研究文章|开放获取</P.。><D.一世v class="sc-kZmsYB doGfnX article_citation"> 体积 2020. <span class="sc-iSDuPN ezntTT">|</S.。P.。an>文章ID. 6975250 <span class="sc-iSDuPN ezntTT">|</S.。P.。an> <a class="sc-htpNat bUhGXt link sc-fZwumE dqIsrA" href="https://doi.org/10.1155/2020/6975250" aria-label="Doi-link">https://doi.org/10.1155/2020/6975250</a> </div> <div class="sc-kaNhvL kwRfSr article_full_citation"> <div class="sc-iBEsjs ezuwCV isHide"> <p>薛阳，志良朱，海宇，yuli zhao那 “<S.。P.。an class="adjust-article-svg-size">基于命名基于游戏的社交网络信息源位置的方法</S.。P.。an>“，<i>复杂</一世>那 卷。2020.那 文章ID.6975250那 8.   页面那 2020.． https://doi.org/10.1155/2020/6975250</P.。></D.一世v> <button class="sc-hSdWYo etauus sc-LKuAh fxGnqr" color="">显示引文</button> </div> <h1 class="sc-iRbamj jZOxOO sc-RcBXQ goubQH article_title adjust-article-svg-size heading-title">基于命名基于游戏的社交网络信息源位置的方法</h1> </div> <div class="sc-gPzReC fMlAsT article_authors"> <hr class="sc-fHxwqH kHliir hr__author"> <span class="">雪阳那<S.。你P.>1那2</S.。你P.></S.P.an> <span class=""><b>Zhiliang Zhu.</b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-jrIrqw eeUyzW icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><a class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0003-3450-1711" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-hjRWVT femdCr" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a>那<S.。你P.>1</S.。。你P.></S.P.an> <span class="">海玉<a class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0001-5951-2332" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-hjRWVT femdCr" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a>那<S.。你P.>1</S.。。你P.>和</S.。P.。an> <span class="">余莉赵<S.。你P.>1</S.。。你P.></S.P.an> <div class="sc-iQtOjA llLcVY isHide"> <p><sup>1</S.。你P.><S.P.an>2 .东北大学软件学院，辽宁沈阳110819</S.。P.。an></p> <p><sup>2</S.。你P.><S.P.an>2 .鞍山师范学院数学与信息科学学院，鞍山114005</S.。P.。an></p> </div> <button class="sc-hSdWYo etauus sc-iybRtq clzRlh" color="">展示更多</button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</b>Dimitrios Stamovlasis</D.一世v> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</S.。P.。an> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">02年1月20日</S.。P.。an> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">公认</S.。P.。an> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2020年04月01</S.。P.。an> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</S.。P.。an> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2020年4月27日</S.。P.。an> </div> </div> </div> <article class="sc-jeCdPy gaWrER article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">抽象的</h4> <p>本文研究了基于网络拓扑和一组观测数据的社会网络中信息传播源的定位问题。我们提出了一种简洁新颖的方法，利用命名博弈论准确地定位信息的来源。本研究介绍了一种动态部署方法的设计，大大减少了观测次数和定位源所需的时间。此外，它根据观测提供的信息计算每个节点作为源的概率。该方法可以潜在地应用于各种信息传播模型。仿真结果表明，该方法能够在距离真实源较短的跳数内估计出信息源。</P.。><S.。P.。an class="end-abs"></span> <h4 id="introduction">1.介绍</h4> <p>社交软件的普及增加了用户对信息的访问，提高了信息传播的速度。这种社交软件不仅方便了我们的日常生活，也让我们容易受到风险的影响。例如，误导性的信息会促使人们做出错误的判断，甚至危及社会安全和稳定[<a href="#B1">1</a>]．为了控制误导信息的出现和传播，并减少由它们造成的损坏，准确定位信息源很重要。</P.。><P.。>许多关于信息传播的先前研究研究集中在信息来源的本地上。其中大多数基于对网络结构的有限知识和一些节点的状态。早期的方法旨在在树状网络上工作。他们依靠识别网络中的跨越树，并将跨越树的根源视为传播源[<a href="#B2">2</a>-<a href="#B4">4.</a>]．Dariusz等[<a href="#B5">5.</a>]分析了三家Twitter网络的谣言源头检测。本研究描述了一个寻找谣言讲话者位置和计算传播路径长度的实证调查。此外，还有一些方法是基于网络拓扑结构的节点中心度测量来检测谣言源。例如，沙阿和扎曼[<a href="#B6">6.</a>]提出了谣言中心，以识别谣言源，并声称具有最大闭合中心的节点是谣言源。朱和莹[<a href="#B7">7.</a>]证明谣言来源为感染偏心度最小的约旦感染中心。随后，Chen等人[<a href="#B8">8.</a>]扩展了Jordan Center技术来检测多个谣言源。王[<a href="#B9">9.</a>]采用了一种新的反向传播方法，缩小了可疑来源的规模，并引入了一个时变社交网络中谣言传播的分析模型。Shelke和Attar [<a href="#B10">10</a>]基于节点通知时间与源-节点测地线距离的正相关关系计算Spearman中心性。该算法具有较高的定位精度和较低的时间复杂度。Jiang等人[<a href="#B11">11</a>]开发了一种算法来估计感染源的数量未知的时间戳子集。此外，还证明了所采用的算法可以估计单源和多源。</P.。><P.。>为了提高本地化准确性，许多以前的方法基于观察获得了传播过程的信息。各种观察范围导致了该领域各种方法的出现[<a href="#B12">12</a>]．根据文献，有三个主要类别的观察[<a href="#B13">13</a>]．(1)完整观察:给定时间<一世>T.</一世>在传播期间，这种类型的观察显示了网络中每个节点的确切状态[<a href="#B13">13</a>]．（2）快照观察：快照在给定时间提供网络状态的部分了解<一世>T.</一世>[<a href="#B14">14</a>]．例如，它可以识别所有受感染的节点或仅识别一组节点。(3)传感器观测:传感器记录了传播的细节，包括观测状态、状态转换时间和传播方向[<a href="#B15">15</a>]．然而，由于社交网络的大规模，很难应用上面提到的方法来在现实世界信息传输过程中设定观察。</P.。><P.。>在这项研究中，我们提出了一种新颖的观察设置方法，这些方法受到命名博弈论的启发[<a href="#B16">16</a>那<a href="#B17">17</a>]．根据节点之间的交互，命名游戏模拟了用单个单词命名对象的过程[<a href="#B18">18</a>那<a href="#B19">19</a>]．具体地，选择用于对话目的的一对相邻节点，由此其中一个是扬声器，另一个是收听者。扬声器和听众都有记忆。最初，扬声器从内存中选择一个单词，并将其发送到侦听器作为未知对象的名称。如果在侦听器的内存中也存在发送字，则两个节点达成共识。因此，只有两个节点都会保持该词。相比之下，如果侦听器没有在内存中发射字，则对话将失败，并且侦听器将学习该单词并将其存储到内存中。该过程持续直到（a）最终收敛到从整个群体或（b）到单个单词，直到该过程在足够长的通信时失败。</P.。><P.>与命名游戏类似，信息传播依赖于个体之间的交互。在社交网络中，个人可以记住他们的邻居是否传播了信息，如果是，他们知道传播时间。因此，在我们的观察设置方法中，如果一个人被选择为观察对象，它就被定义为命名游戏中的说话人。因此，这个人将最先传播信息的邻居透露给听者。基于观测结果提供的内容，我们设计了一种基于多次迭代定位信息传播源的方法。我们更新了在每次迭代中作为源的每个节点的概率。我们的方法是在定位源的过程中引入观测设置，而不是在定位的开始阶段。这种方法的优点在于，我们可以使用尽可能少的观测来实现更高的源定位精度。</P.。><P.>本研究的目的是在尽可能少的观测下准确定位传播源。因此，我们设计了一种根据需要建立观测的方法。该研究不是专注于每个观察对象的特定状态，而是专注于其邻近对象的状态。该方法不需要知道传播过程的参数，也不局限于传播的类型。本研究为定位传播源提供了一种新的方法，取得了较好的精度。</P.。><P.。>本研究的其余部分组织如下。部分<a href="#sec2">2</a>用命名游戏介绍社交网络中信息源位置的模型。部分<a href="#sec3">3.</a>通过分析和比较描述模拟结果。部分<a href="#sec4">4.</a>是结论部分。</P.。><h4 id="materials-and-methods">2。材料和方法</h4> <p>在本节中，我们将简要介绍有关信息源位置的基本知识，包括网络结构和经典的传播模型。随后，我们应用命名博弈论来定位唯一的信息源。</P.。><h5 id="sec2.1">2．1．网络结构与经典传播模型</h5> <p>通常，一个过程在其中传播的网络被建模为无向无权图。用<S.。P.。an class="inline_break"> <svg height="11.5564pt" id="M1" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 40.952 11.5564" width="40.952pt" 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="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z" id="g113-72"></path> </g> <g 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-41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path> </g> </svg></span>是否节点集和<一世>E.。</一世>表示节点之间的链接。基于这些接触网络的经典传播模型，如SI [<a href="#B20">20.</a>),姐姐(<a href="#B21">21</a>，和SIR [<a href="#B22">22</a>]，已经被调查过。然而，真实信息传播比经典模型要复杂得多，并且在定位信息源时难以预先了解传播模型。我们假设传播过程<S.。vg height="8.8423pt" id="M3" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.02496 8.8423" width="9.02496pt" 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="#g113-72"></use> </g> </svg>遵循三个模型中的任何一个。然后选择一个节点作为信息传播源(表示为<一世>S.。</一世>）.信息从<一世>S.。</一世>并在网络中快速传播。不知道传播动态和任何参数，我们的方法可以估计信息传播的源。</P.。><h5 id="sec2.2">2.2。找到信息源</h5> <p>在本节中，我们提出了一种基于命名游戏的方法，该方法可以基于通信交互在底层拓扑上自然地定位源节点。我们假设检测传播源的个人或组织可以与网络中的所有节点通信。可以认为是与网络中所有节点相连的一个额外节点，用<一世>N</一世>∗。让<一世>S.。</一世>代表一个随机变量，其先前分配在节点集上均匀<S.。P.。an class="nowrap"> <svg height="6.04987pt" id="M4" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg>．</S.。P.。an>有效地，这意味着网络中的任何节点都同样可能是源。我们的目标是找到未知的源节点<一世>S.。</一世>在一定时间内，不管采用哪种信息传播模型。我们表示<S.。vg height="15.7176pt" id="M5" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 82.6408 15.7176" width="82.6408pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.524,0)"> <path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path> </g> <g transform="matrix(.013,0,0,-0.013,16.957,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.087,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.35,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.861,0)"> <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> <g transform="matrix(.0091,0,0,-0.0091,48.245,3.132)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> </g> <g transform="matrix(.013,0,0,-0.013,51.301,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.799,0)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.232,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.73,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.241,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.241,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,71.789,3.784)"> <path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,77.349,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>作为概率向量，因此<一世>P.。</一世><S.你b><i>一世</一世></S.你b>（<一世>T.</一世>）表示节点的概率<一世>一世</一世>传播源在<一世>T.-</一世>迭代。最初,∀<一世>一世</一世>∈{1,2,…,<一世>N</一世>}，<一世>P.。</一世><S.你b><i>一世</一世></S.你b>（0）等于1 /<一世>N</一世>．</P.。><P.。>在每一个时间步<一世>T.</一世>，我们设计了一种更新价值的方法<S.。P.。an class="nowrap"> <svg height="11.5564pt" id="M6" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 21.6301 11.5564" width="21.6301pt" 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="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <use 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> </svg>．原来，<一世>C</一世>=<一世>V。</一世>的节点<一世>NS.</一世><S.你b><i>T.</一世></S.你b>从<一世>C</一世>在它被选为演讲者之后。同时，发言者节点<一世>NS.</一世><S.你b><i>T.</一世></S.你b>也是一个观察。观察结果有助于我们有效地获得传播信息并准确地定位源节点。我们将本地来源定义为首先将信息传播到观察的节点。在信息传播的场景中，个人知道哪个邻居是其本地来源。因此，扬声器<一世>NS.</一世><S.你b><i>T.</一世></S.你b>告诉听众<一世>N</一世>∗其本地来源。我们假定所有的发言者都是诚实的。这意味着信息<一世>NS.</一世><S.你b><i>T.</一世></S.你b>转移到<一世>N</一世>*是真实的。与其他类型的设定观察方法相比，我们的方法事先没有确定所有观察，但它证实了在每次迭代时的观察。然后，我们让<一世>F</一世><S.你b><i>T.</一世></S.你b>={<一世>F</一世><S.你b><i>T.</一世>1</S.。。你b>、……<一世>F</一世><S.你b><i>T.</一世>|<一世>F<S.。。你b>T.</S.。你b></i>|</S.。你b>}<S.。vg height="7.88973pt" id="M9" style="vertical-align:-0.6370101pt" version="1.1" viewbox="-0.0498162 -7.25272 7.75925 7.88973" width="7.75925pt" 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="#g117-77"></use> </g> </svg> <svg 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xlink:href="#B14-3"></use> </svg></span></span>在哪里<S.。vg height="9.34337pt" id="M15" style="vertical-align:-3.382461pt" version="1.1" viewbox="-0.0498162 -5.96091 11.6957 9.34337" width="11.6957pt" 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="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.461,3.132)"> <use xlink:href="#g50-123"></use> </g> </svg>表示不属于的节点数<S.。vg height="10.7866pt" id="M16" style="vertical-align:-2.150701pt" version="1.1" viewbox="-0.0498162 -8.6359 9.52083 10.7866" width="9.52083pt" 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="#g113-82"></use> </g> </svg>它们在时刻是非零概率的源<一世>T.</一世>．此外,<一世>问：</一世>是一组在不同情况下具有不同内容的节点，并且表示为<S.。P.。an class="equation_break" id="EEq2"><span class="left_break" id="L17"></span><span class="middle_break"><span class="center_break" id="M17"> <svg height="36.3978pt" id="M17-1" version="1.1" viewbox="0 0 125.354 36.3978" width="125.354pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B17-1"> <g transform="matrix(.013,0,0,-0.013,0,21.526)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.02,21.526)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.28,21.526)"> <path d="M533 -990V-954C407 -937 392 -869 392 -793L412 76C412 166 380 246 300 269V273C381 294 412 374 412 463C412 753 392 1055 392 1340C392 1413 407 1477 533 1494V1530C445 1530 317 1507 317 1312L327 436C327 378 321 302 144 292V248C321 238 327 162 327 104L317 -778C317 -970 445 -990 533 -990Z" id="g119-167"></path> </g> <g transform="matrix(.013,0,0,-0.013,32.87,11.011)"> <path d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 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transform="matrix(.0091,0,0,-0.0091,56.71,14.142)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.01,11.011)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.27,11.011)"> <path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z" id="g113-243"></path> </g> <g transform="matrix(.013,0,0,-0.013,82.62,11.011)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.87,31.65)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.94,34.782)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.51,31.65)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.05,31.65)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,62.83,34.782)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.5,31.65)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.82,31.65)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,79.89,34.782)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.86,31.65)"> <use xlink:href="#g117-145"></use> </g> <g transform="matrix(.013,0,0,-0.013,87.19,31.65)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,98.48,31.65)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,122.39,21.526)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R17"> <svg class="label" height="11.44pt" id="M17-2" 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="B17-2"> <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></p> <p>根据局部源集<一世>S.。</一世><S.你b><i>T.</一世></S.你b>并且网络拓扑，可以确定一些边缘的传播方向。方向表示信息可以从起始节点传播到结束节点。我们让我们<一世>CF。</一世><S.你b><i>T.</一世></S.你b>={<一世>CF。</一世><S.你b><i>T.</一世>1</S.。。你b>、……<一世>CF。</一世><S.你b><i>T.</一世>|<一世>CF。<S.。。你b>T.</S.。你b></i>|</S.。你b>}<S.。vg height="7.88973pt" id="M18" style="vertical-align:-0.6370101pt" version="1.1" viewbox="-0.0498162 -7.25272 7.75925 7.88973" width="7.75925pt" 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="#g117-77"></use> </g> </svg> <svg height="8.8423pt" id="M19" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.35121 8.8423" width="9.35121pt" 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="#g113-87"></use> </g> </svg>表示包含观察节点的共同邻居的集合<一世>NS.</一世><S.你b><i>T.</一世></S.你b>及其本地来源。如果<S.。P.。an class="nowrap"> <svg height="12.3916pt" id="M20" style="vertical-align:-3.42948pt" version="1.1" viewbox="-0.0498162 -8.96212 41.1997 12.3916" width="41.1997pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.293,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.079,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.051,0)"> <use xlink:href="#g117-145"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.378,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.67,0)"> <use xlink:href="#g113-243"></use> </g> </svg>那</S.。P.。an>传播方向必须从中节点开始<一世>S.。</一世><S.你b><i>T.</一世></S.你b>对共同的邻居。因此，我们通过删除信息传播的不可能的边缘来将无向导的图形转换为定向图。具体而言，如果<一世>S.。</一世><S.你b><i>T.</一世></S.你b>=<一世>φ.</一世>，从的邻接点开始的边<一世>NS.</一世><S.你b><i>T.</一世></S.你b>应该被删除。否则,如果<一世>S.。</一世><S.你b><i>T.</一世></S.你b><i>≠</一世><一世>φ.</一世>，其开始节点在<一世>F</一世><S.你b><i>T.</一世></S.你b><i>- s</一世><S.你b><i>T.</一世></S.你b>，且其目标节点在<一世>S.。</一世><S.你b><i>T.</一世></S.你b>设置应被删除。此外,如果|<一世>S.。</一世><S.你b><i>T.</一世></S.你b>| > 1, the edges whose start and target nodes are all in<一世>S.。</一世>应该被删除。说明边缘方向的确定过程的一个简单示例如图所示<a href="//www.newsama.com/journals/complexity/2020/6975250/fig1/" target="_blank">1</a>（一种）-<a href="//www.newsama.com/journals/complexity/2020/6975250/fig1/" target="_blank">1</a>（d）。绿色节点<S.。vg height="6.04987pt" id="M21" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>1</S.。你b>是一个被视为观察的扬声器。橙色节点<S.。vg height="6.04987pt" id="M22" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>和<S.。vg height="6.04987pt" id="M23" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>6.</S.。你b>是本地节点的来源<S.。vg height="6.04987pt" id="M24" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>1</S.。你b>．节点<S.。vg height="6.04987pt" id="M25" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>和<S.。vg height="6.04987pt" id="M26" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>6.</S.。你b>同时传播信息，所以边在节点之间<S.。vg height="6.04987pt" id="M27" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>和<S.。vg height="6.04987pt" id="M28" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>6.</S.。你b>可以删除。节点<S.。vg height="6.04987pt" id="M29" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>5.</S.。你b>是节点的常见邻居<S.。vg height="6.04987pt" id="M30" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>1</S.。你b>和<S.。vg height="6.04987pt" id="M31" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>．节点<S.。vg height="6.04987pt" id="M32" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>5.</S.。你b>必须在节点之前传播信息<S.。vg height="6.04987pt" id="M33" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>，所以节点之间边缘的方向<S.。vg height="6.04987pt" id="M34" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>5.</S.。你b>和节点<S.。vg height="6.04987pt" id="M35" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>必须从<S.。vg height="6.04987pt" id="M36" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>3.</S.。你b>来<S.。vg height="6.04987pt" id="M37" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>5.</S.。你b>．类似地，节点之间边缘的方向<S.。vg height="6.04987pt" id="M38" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>6.</S.。你b>和<S.。vg height="6.04987pt" id="M39" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>4.</S.。你b>必须从<S.。vg height="6.04987pt" id="M40" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>6.</S.。你b>来<S.。vg height="6.04987pt" id="M41" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg><sub>4.</S.。你b>．</P.。><D.一世v class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="6975250.fig.001" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.001.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 边缘传播方向的确定过程说明。</D.一世v> </div> </div> </div> <p>我们表示[<一世>你</一世>那<S.。vg height="6.04987pt" id="M42" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg>]作为节点之间的最短路径<一世>你</一世>和<S.。P.。an class="nowrap"> <svg height="6.04987pt" id="M43" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg>．</S.。P.。an>让<一世>D.</一世>（<一世>你</一世>那<S.。P.。an class="nowrap"> <svg height="6.04987pt" id="M44" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg>）</S.。P.。an>为两者之间最短路径的长度<一世>你</一世>和<S.。vg height="6.04987pt" id="M45" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="#g185-40"></use> </g> </svg>在<S.。P.。an class="nowrap"> <svg height="8.8423pt" id="M46" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.02496 8.8423" width="9.02496pt" 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="#g113-72"></use> </g> </svg>．</S.。P.。an>很明显每个节点<一世>S.。</一世><S.你b><i>tr</一世></S.你b>在<一世>S.。</一世><S.你b><i>T.</一世></S.你b>早先接收信息<一世>NS.</一世><S.你b><i>T.</一世></S.你b><i>．</一世>什么时候<一世>D.</一世>（<一世>一世</一世>那<一世>NS.</一世><S.你b><i>T.</一世></S.你b>）= inf或<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>tr</一世></S.你b>= inf，表示该节点<一世>一世</一世>无法将信息传播到观察<一世>N</一世><S.你b><i>圣</一世></S.你b>．因此，节点<一世>一世</一世>一定不是传播源，我们更新值<S.。vg height="11.5564pt" id="M47" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 21.6301 11.5564" width="21.6301pt" 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="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.524,0)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.957,0)"> <use xlink:href="#g113-42"></use> </g> </svg>根据(<a href="#EEq1">1</a>）.什么时候<一世>D.</一世>（<一世>一世</一世>那<一世>NS.</一世><S.你b><i>T.</一世></S.你b>）<一世>≠</一世>正,<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>tr</一世></S.你b>）<一世>≠</一世>正,我们表示<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>T.</一世></S.你b>）作为从节点的距离<一世>一世</一世>设置<一世>S.。</一世><S.你b><i>T.</一世></S.你b>．可以用<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>T.</一世></S.你b>) = max (<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>tr</一世></S.你b>））对所有人<一世>S.。</一世><S.你b><i>tr</一世></S.你b> ∈ <一世>S.。</一世><S.你b><i>T.</一世></S.你b>．此外，如果演绎之间<一世>D.</一世>（<一世>一世</一世>那<一世>NS.</一世><S.你b><i>T.</一世></S.你b>),<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>T.</一世></S.你b>)大于零，则节点在<一世>S.。</一世><S.你b><i>T.</一世></S.你b>会收到节点之前的信息<一世>NS.</一世><S.你b><i>T.</一世></S.你b>．因此，扣除的较大值<一世>D.</一世>（<一世>一世</一世>那<一世>NS.</一世><S.你b><i>T.</一世></S.你b>),<一世>D.</一世>（<一世>一世</一世>那<一世>S.。</一世><S.你b><i>T.</一世></S.你b>）提供更大的节点概率<一世>一世</一世>作为传播源。如果<一世>S.。</一世><S.你b><i>T.</一世></S.你b><i>≠</一世><一世>φ.</一世>，我们更新概率<S.。P.。an class="equation_break" id="EEq3"><span class="left_break" id="L48"></span><span class="middle_break"><span class="center_break" id="M48"> <svg height="71.9511pt" id="M48-1" version="1.1" viewbox="0 0 26.058 71.9511" width="26.058pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-1"> <g transform="matrix(.013,0,0,-0.013,0,39.303)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.38,42.435)"> <use xlink:href="#g50-106"></use> </g> <g 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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="93.9662pt" id="IL48" version="1.1" viewbox="0 0 14.93 93.9662" 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 41.05)" xlink:href="#B48-3"></use> </svg></span></span>在哪里<一世>ɛ</一世>是之间的最小差异<一世>NS.</一世><S.你b><i>T.</一世></S.你b>和<一世>S.。</一世><S.你b><i>T.</一世></S.你b>每一个<一世>一世</一世>谁的<一世>P.。</一世><S.你b><i>一世</一世></S.你b>（<一世>T.</一世>） <一世>≠</一世>0。如图所示<a href="//www.newsama.com/journals/complexity/2020/6975250/fig1/" target="_blank">1</a>（e）可以看出，节点4和5不能将信息传播到本地源3和6.然后，我们计算节点1,2,3和7之间的距离差，观察到其本地源，分别。之后，我们计算根据等式的源代码的可能性（<a href="#EEq3">3.</a>）.最后，我们得出结论，节点7是源。</P.。><P.。>一般情况下，需要多次观测才能准确定位信息源。因此，我们定义了set<一世>m</一世>（<一世>T.</一世>）包含具有最高源节点的概率的节点索引。因此，我们有<S.。P.。an class="inline_break"> <svg height="14.8173pt" id="M49" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 91.063 14.8173" width="91.063pt" 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="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 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<g transform="matrix(.013,0,0,-0.013,92.52,9.491)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.39,9.308)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R50"> <svg class="label" height="11.44pt" id="M50-3" 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="B50-3"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <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,-0.013,10.96,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>其中A为常数整数，大于单位，定义为迭代结果不变的次数。对算法中提出的信息源定位方法进行了总结<a href="//www.newsama.com/journals/complexity/2020/6975250/alg1/" target="_blank">1</a>．</P.。><D.一世v class="floats-partial-section partial-other-wrapper" data-section="alg1"> <div class="floats-partial-content fig-content-alg1"> <table class="algorithm-group"> <tbody> <tr> <td> <table class="algorithm" id="alg1"> <tbody> <tr> <td></td> <td>输入：一个无向和未加权的图表<S.。P.。an class="nowrap"> <svg height="11.5564pt" id="M51" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 55.9008 11.5564" width="55.9008pt" 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="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,14.699,0)"> <path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,25.962,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,30.46,0)"> <path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,37.988,0)"> <path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path> </g>  <g transform="matrix(.013,0,0,-0.013,43.131,0)"> <path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,51.139,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path> </g> </svg>那</S.。P.。an>一种。</T.D.></T.r> <tr> <td></td> <td>而<S.。vg height="12.3916pt" id="M52" style="vertical-align:-3.42948pt" version="1.1" viewbox="-0.0498162 -8.96212 31.1121 12.3916" width="31.1121pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,19.989,0)"> <path d="M-161 592L-215 609L-427 -83L-372 -100L-161 592Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,12.316,0)"> <path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,23.608,0)"> <path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path> </g> </svg>做</T.D.></T.r> <tr> <td></td> <td>输入:扬声器节点<一世>NS.</一世><S.你b><i>t。</一世></S.你b></td> </tr> <tr> <td></td> <td>更新<S.。vg height="11.5564pt" id="M53" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 21.6301 11.5564" width="21.6301pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,12.524,0)"> <path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,16.957,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path> </g> </svg>根据等式（<a href="#EEq1">1</a>）</T.D.></T.r> <tr> <td></td> <td> Transform the undirected graph to a directed graph.</T.D.></T.r> <tr> <td></td> <td> if<一世>S.。</一世><S.你b><i>T.</一世></S.你b><i>≠ϕ</一世></T.D.></T.r> <tr> <td></td> <td>为<一世>一世</一世>= 1: |<一世>S.。</一世><S.你b><i>T.</一世></S.你b><i>|</一世>做</T.D.></T.r> <tr> <td></td> <td> Update the value of<S.vg height="11.5564pt" id="M54" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 21.6301 11.5564" width="21.6301pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,12.524,0)"> <path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,16.957,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path> </g> </svg>根据等式（<a href="#EEq3">3.</a>）</T.D.></T.r> <tr> <td></td> <td> end for</T.D.></T.r> <tr> <td></td> <td> end if</T.D.></T.r> <tr> <td></td> <td> if<一世>P.。</一世>（<一世>T.</一世>）满足<一世>m</一世>（<一世>T.</一世>）</T.D.></T.r> <tr> <td></td> <td>中断while循环</T.D.></T.r> <tr> <td></td> <td> end if</T.D.></T.r> <tr> <td></td> <td>结束时</T.D.></T.r> <tr> <td></td> <td>输出:<一世>m</一世>（<一世>T.</一世>）</T.D.></T.r> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">算法1</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/alg1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 信息源的本地化。</D.一世v> </div> </div> </div> <h4 id="simulation-results">3.仿真结果</h4> <p>为了评估所提算法的性能，我们考虑了表中列出的四个真实的社交网络<a href="//www.newsama.com/journals/complexity/2020/6975250/tab1/" target="_blank">1</a>．安然的电子邮件[<a href="#B23">23</a>数据集包含了143个用户2001年的电子邮件交谈记录。另外三个是来自三个不同地区的Facebook数据集。这四个选定的数据集可以在网站上找到<a href="http://networkrepository.com/" target="_blank">http://networkrepository.com/</a>．在我们的方法中，一些边缘的传播方向是根据观测提供的信息确定的。边缘的方向确定得越多，得到的结果就越准确。因此，选择能够确定更多边缘方向的节点作为观测值比较好，比如度大的节点和聚类系数大的节点。在不失一般性的情况下，我们随机选择一个节点作为传播消息的源，并在500次运行中对源进行本地化。与Jiang等人的工作类似[<a href="#B13">13</a>，参数设置为<一世>α.。</一世>= 0.75,<一世>β</一世>= 0.5。我们提出的方法不关注节点的状态转移。因此，可以应用它来定位源，而不考虑传播模型。为了说明所提出的方法能够更准确地定位源，我们从上述四个社会网络中选择了SIS传播模型，据此<S.。P.。an class="inline_break"> <svg height="16.3701pt" id="M55" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -12.4266 56.422 16.3701" width="56.422pt" 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="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z" id="g117-91"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.263,0)"> <path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 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class="isep"></span> <svg height="16.3701pt" style="vertical-align:-3.9435pt" version="1.1" viewbox="138.3671838 -12.4266 66.29 16.3701" width="66.29pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,138.417,0)"> <use xlink:href="#g113-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,144.891,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,150.853,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,161.389,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,165.887,0)"> <use xlink:href="#g113-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,172.361,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,178.322,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,188.859,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,195.099,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,199.597,0)"> <use xlink:href="#g113-42"></use> </g> </svg></span>是平均聚类系数，和<一世>m</一世><S.你b><i>一世</一世></S.你b>表示之间的链接数<一世>一世</一世>的朋友。此外,<S.。vg height="21.4656pt" id="M57" style="vertical-align:-12.17727pt" version="1.1" viewbox="-0.0498162 -9.28833 97.0004 21.4656" width="97.0004pt" 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="#g117-91"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.263,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.11,0)"> <use xlink:href="#g117-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.741,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.004,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.515,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.73,0)"> <use xlink:href="#g113-9"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.149,0)"> <use xlink:href="#g121-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.757,0)"> <use xlink:href="#g121-95"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.464,0)"> <use xlink:href="#g121-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.181,8.345)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.73,8.345)"> <path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,61.886,8.345)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.8,8.345)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,71.069,8.345)"> <path d="M735 650H491L482 618L516 614C568 608 571 595 541 535L299 115H297L196 559C187 600 195 608 238 614L265 618L275 650H26L18 618C79 611 98 605 115 527L234 -9H272C389 197 542 449 591 523C647 608 656 612 726 618L735 650Z" id="g50-87"></path> </g> <g transform="matrix(.013,0,0,-0.013,78.71,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,85.86,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,87.742,3.132)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.177,0)"> <use xlink:href="#g113-126"></use> </g> </svg>是网络直径，和<一世>D.</一世><S.你b><i>ij</一世></S.你b>表示最短路径连接节点上的边数<一世>一世</一世>和<一世>j</一世>．</P.。><D.一世v class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr class="thead"> <td class="align_left">网络</T.D.><T.D.Class="align_center">类型</T.D.><T.D.Class="align_center">N</T.D.><T.D.Class="align_center">m</T.D.><T.D.Class="align_center"><<一世>K.</一世>></T.D.><T.D.Class="align_center"><<一世>C</一世>></T.D.><T.D.Class="align_center"><<一世>D.</一世>></T.D.></T.r> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr> <td class="align_left">安然</T.D.><T.D.Class="align_center">und</T.D.><T.D.Class="align_center">143</T.D.><T.D.Class="align_center">623.</T.D.><T.D.Class="align_center">8.713</T.D.><T.D.Class="align_center">0.453</T.D.><T.D.Class="align_center">8.</T.D.></T.r> <tr> <td class="align_left">Simmons81.</T.D.><T.D.Class="align_center">und</T.D.><T.D.Class="align_center">1510.</T.D.><T.D.Class="align_center">32984</T.D.><T.D.Class="align_center">43.687</T.D.><T.D.Class="align_center">0.325</T.D.><T.D.Class="align_center">7.</T.D.></T.r> <tr> <td class="align_left">汉密尔顿46.</T.D.><T.D.Class="align_center">und</T.D.><T.D.Class="align_center">2312</T.D.><T.D.Class="align_center">96393</T.D.><T.D.Class="align_center">83.385</T.D.><T.D.Class="align_center">0.302</T.D.><T.D.Class="align_center">6.</T.D.></T.r> <tr> <td class="align_left">Wake73</T.D.><T.D.Class="align_center">und</T.D.><T.D.Class="align_center">5366</T.D.><T.D.Class="align_center">279186</T.D.><T.D.Class="align_center">104.057</T.D.><T.D.Class="align_center">0.279</T.D.><T.D.Class="align_center">9.</T.D.></T.r> <tr class="table-tr"> <td colspan="7"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 真实网络数据集网络特征的比较。</D.一世v> </div> </div> </div> <h5 id="sec3.1">3．1．信息来源定位的准确性</h5> <p>我们使用真实源和估计源之间的误差和平均误差距离来证明我们在Section中提出的方法的准确性<a href="#sec2">2</a>．我们表示通过实际和估计源之间跳跃的最短距离的误差距离<一世>φ.</一世>[<a href="#B24">24</a>]．由于减小了ϕ的值，该方法实现的性能得到了提高。具体而言，如果<一世>φ.</一世>= 0时，我们的方法准确识别了真实的源节点。数字<a href="//www.newsama.com/journals/complexity/2020/6975250/fig2/" target="_blank">2</a>显示四个真实社交网络中误差距离的分布。当参数a = 1时，我们的方法在安龙网络的情况下实现了50％的准确性，在SimMons81网络的情况下，78％，在Hamilton46网络的情况下为87％，而84％Wake73网络。随着增加的值，算法的准确性逐渐提高。</P.。><D.一世v class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="(一)“Name="6975250.fig.002a" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002a.svgz"> <br> <strong>(一)</S.。T.rong> </div> <div class="partial-carousel--single-image"> <img alt="(b)“Name="6975250.fig.002b" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002b.svgz"> <br> <strong>(b)</S.。T.rong> </div> <div class="partial-carousel--single-image"> <img alt="(c)“Name="6975250.fig.002c" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002c.svgz"> <br> <strong>(c)</S.。T.rong> </div> <div class="partial-carousel--single-image"> <img alt="(d)“Name="6975250.fig.002d" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002d.svgz"> <br> <strong>(d)</S.。T.rong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig2"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)“Name="6975250.fig.002a" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002a.svgz"><br><strong>(一)</S.。T.rong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)“Name="6975250.fig.002b" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002b.svgz"><br><strong>(b)</S.。T.rong></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)“Name="6975250.fig.002c" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002c.svgz"><br><strong>(c)</S.。T.rong></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)“Name="6975250.fig.002d" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.002d.svgz"><br><strong>(d)</S.。T.rong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig2"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 不同数据集中的错误距离分布(ϕ): (a) Enron， (b) Simmons81， (c) Hamilton46， (d) Wake73。</D.一世v> </div> </div> </div> <p>数字<a href="//www.newsama.com/journals/complexity/2020/6975250/fig3/" target="_blank">3.</a>为与a值的平均误差距离，由图可知<a href="//www.newsama.com/journals/complexity/2020/6975250/fig3/" target="_blank">3.</a>平均误差距离随A减小。因此，增加A可以更准确地定位源。</P.。><D.一世v class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="6975250.fig.003" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.003.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 四个社交网络的平均误差距离。</D.一世v> </div> </div> </div> <h5 id="sec3.2">3.2。提出方法的效率</h5> <p>在我们的方法中，时间复杂度o（<一世>N</一世>·<一世>R.。</一世>），其中<一世>R.。</一世>是观测的数量。因此，应使用观测数来评估我们所提出的信息源定位方法的有效性。这是由于这样一个事实，即随着观察数量的增加，需要的迭代数量也随之增加，因此需要花费更多的时间。我们希望通过选择较少的观测值来准确地定位源节点。因此，观测次数越少，效率越高。对应于图中的精度图<a href="//www.newsama.com/journals/complexity/2020/6975250/fig2/" target="_blank">2</a>,图<a href="//www.newsama.com/journals/complexity/2020/6975250/fig4/" target="_blank">4.</a>显示四个社交网络中节点总数的平均观察次数（百分比）。随着增加的，我们可以看到算法的准确性改善，并且平均观察数增加。此外，当A = 6时，在ENRON网络的情况下，在SIMMONS81网络的情况下，在SIMMONS81网络的情况下，我们所需的平均观测数量小于0.12，在Hamilton46网络的情况下为0.01，在此情况下为0.025Wake73网络。</P.。><D.一世v class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="6975250.fig.004" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.004.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 四家社交网络的平均观察百分比。</D.一世v> </div> </div> </div> <p>4个社交网络中，当A = 3时，观察的百分比如图所示<a href="//www.newsama.com/journals/complexity/2020/6975250/fig5/" target="_blank">5.</a>， B是实验的次数。结果表明，即使我们随机选择相同的观测数，也能获得不同的精度。因此，不同的观测结果对结果的准确性有相当大的影响。数据<a href="//www.newsama.com/journals/complexity/2020/6975250/fig5/" target="_blank">5(一个)</a>-<a href="//www.newsama.com/journals/complexity/2020/6975250/fig5/" target="_blank">5 (d)</a>表明每个点的波动范围显着降低，黄点的数量显着增加。这表明网络结构对结果具有相当大的影响。</P.。><D.一世v class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="(一)“Name="6975250.fig.005a" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005a.svgz"> <br> <strong>(一)</S.。T.rong> </div> <div class="partial-carousel--single-image"> <img alt="(b)“Name="6975250.fig.005b" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005b.svgz"> <br> <strong>(b)</S.。T.rong> </div> <div class="partial-carousel--single-image"> <img alt="(c)“Name="6975250.fig.005c" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005c.svgz"> <br> <strong>(c)</S.。T.rong> </div> <div class="partial-carousel--single-image"> <img alt="(d)“Name="6975250.fig.005d" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005d.svgz"> <br> <strong>(d)</S.。T.rong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig5"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)“Name="6975250.fig.005a" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005a.svgz"><br><strong>(一)</S.。T.rong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)“Name="6975250.fig.005b" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005b.svgz"><br><strong>(b)</S.。T.rong></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)“Name="6975250.fig.005c" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005c.svgz"><br><strong>(c)</S.。T.rong></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)“Name="6975250.fig.005d" src="https://static-01.hindawi.com/articles/complexity/volume-2020/6975250/figures/6975250.fig.005d.svgz"><br><strong>(d)</S.。T.rong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig5"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</S.。P.。an> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6975250/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 四个社交网络中的观察百分比：（a）enron，（b）simmons81，（c）Hamilton46和（d）key73。</D.一世v> </div> </div> </div> <p>数据<a href="//www.newsama.com/journals/complexity/2020/6975250/fig2/" target="_blank">2</a>-<a href="//www.newsama.com/journals/complexity/2020/6975250/fig5/" target="_blank">5.</a>表明，具有较大平均聚类系数的网络，平均程度更大，并且较小的直径达到更高的精度，并且与较小的观察结果相关联。这是因为观察可以以更高的平均聚类系数和平均度确定网络中的附加数量的传播方向。随着边缘所确定的方向的数量增加，结果越准确。此外，网络的直径越大，准确地确定传播源的位置所需的方向越大。</P.。><h5 id="sec3.3">3．3.与其他源定位方法的比较</h5> <p>部分的实验结果<a href="#sec3.1">3．1</a>和<a href="#sec3.2">3．2</a>表明，我们的提出方法可以通过几种观察来实现高分辨率的准确性。具体而言，通过随机选择12％的节点作为观察结果，我们所达到的方法的平均误差距离小于0.6跳。但是，以前的工作[<a href="#B15">15</a>]从理论上证明了当观测占比达到20%时，平均误差距离接近3.3跳。在[的工作<a href="#B25">25</a>[当观察比例达到20％时，平均误差距离约为1.1跳。因此，我们所提出的方法优于[<a href="#B15">15</a>那<a href="#B25">25</a>在准确性和所需观察的数量方面。</P.。><h4 id="conclusions-and-future-work">4.结论与未来工作</h4> <p>在这项研究中，我们调查了社交网络中信息来源的本地化问题。我们首先介绍了一种新颖的部署方案，根据需要根据观察的设置，减少了所需观测的数量。然后，我们提出了一种基于命名博弈论的信息源定位方法。在该方法中，基于一些边缘的传播方向的传播方向，从一个无向图形转换网络。因此，通过计算每个节点与观察结果和本地源之间的距离差来估计传播源。实验结果表明，我们的方法可以通过少量观察来实现更好的定位精度。此外，该方法构成了用于信息传播的一般源定位方法，其不受传播模型的限制。因此，这种方法具有良好的实际应用前景。但是，可以完成一些未来的工作来定位社交网络中的信息源。首先，为了实现更好的观察，更好的观察精度，应设计更好的观察选择方法来取代随机选择。 Secondly, we only considered the source localization problem of single-source information propagation. In this sense, future work may investigate the identification of the sources of multiple-source information propagation.</P.><h4 id="data-availability">数据可用性</h4> <p>用于支持本研究结果的数据可根据要求可从相应的作者获得。</P.。><h4 id="conflicts-of-interest">利益冲突</h4> <p>作者声明他们没有利益冲突。</P.。><h4 id="acknowledgments">致谢</h4> <p>国家自然科学基金资助项目(no . 61977014, no . 61603082, no . 61902056, no . 61374178, no . 61402092);中央高校基本科研业务费专项资金(no . N2017016, no . N171704004);教育部网络教育研究中心网络教育研究基金(Qtone education, no . 61402092)批准号2016ZD306);辽宁省博士创业基金资助项目(批准号:2016ZD306);201501141)。</P.。></D.一世v> <div class="xml-content"> <h4 class="references" id="references">参考文献</h4> <ol> <li id="B1">B. Doerr, M. Fouz和T. Friedrich，“为什么谣言在社交网络中传播得如此之快，”<一世>ACM通信</一世>（第55卷第1期)6, pp. 70-75, 2012。<S.。P.。an class="reflinks">视图:<a href="https://doi.org/10.1145/2184319.2184338">出版商的网站</a><span class="sep">|</S.。P.。an><a href="https://scholar.google.com/scholar_lookup?title=Why%20rumors%20spread%20so%20quickly%20in%20social%20networks&author=B. 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Suchecki et al.&publication_year=2018" target="_blank">谷歌学者</a></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4> <p>薛洋等人版权所有©2020这是一篇开放获取的文章<a rel="license" href="http://creativecommons.org/licenses/by/4.0/">创意公共归因许可证</a>，允许在任何媒介上不受限制地使用、分发和复制，只要原稿被适当引用。</P.。></D.一世v> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 kgAKHb hrTitleRef">更多相关文章</h4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 ejXgSO"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-gVLVqr innUZH article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-cBdUnI bmjKRX 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height="24"><span class="sc-gbOuXE SDMqt">订单印刷副本</S.。P.。an><span class="sc-dRFtgE jooXYL">命令</S.。P.。an></span><span class="sc-htoDjs kNoiZu sc-bfYoXt VdeWO right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-cqpYsc krPIEq"> <div class="sc-hBbWxd hdkxPJ"> <div> 的观点<S.。P.。an>131</S.。P.。an> </div> <div> 下载<S.。P.。an>279</S.。P.。an> </div> </div> <div> <div class="sc-dyGzUR cmbuIE"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2020/6975250" data-style="small_circle"></span>引用</D.一世v> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-gkFcWv gXvjfo" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享帖子</h3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2020/6975250&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" 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