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0pt;">随着图论相关理论的兴起，将复杂系统转化为复杂网络图进行研究能够大 大简化分析过程。从而网络中个节点对整个网络或是其他节点的重要程度的定 量化研宄成为了热点问题，现有的研宄主要从三个角度进行研宄，其研宄思路、 评价指标及相关文献如表</span><span style="text-indent: 24pt; font-size: 9pt; font-family: 宋体; letter-spacing: 0pt;">1.1</span><span style="text-indent: 24pt; font-size: 9pt; font-family: 宋体; letter-spacing: 0pt;">所示。</span></p> <p class="NewStyle21" style="margin: 0pt; text-indent: 0pt; line-height: 11pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-weight: bold; font-size: 9pt;">表</span><span style="font-family: 宋体; letter-spacing: 0pt; font-weight: bold; font-size: 9pt;">1.1</span><span style="font-family: 宋体; letter-spacing: 0pt; font-weight: bold; font-size: 9pt;">网络节点重要度研究</span><span style="font-family: 宋体; letter-spacing: 0pt; font-weight: bold; font-size: 9pt;"><o:p></o:p></span></p> <table class="MsoNormalTable" align="center" style="border-collapse:collapse; width:426.2500pt; mso-table-layout-alt:fixed; mso-padding-alt:0.0000pt 5.4000pt 0.0000pt 5.4000pt ; "> <tbody> <tr style="height:21.3500pt; "> <td width="135" valign="center" style="width: 101.75pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">研究方向</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="154" valign="center" style="width: 115.7pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">方法原理</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="190" valign="center" style="width: 142.55pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">重要度评价指标</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="88" valign="center" style="width: 66.25pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:15.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">相关文献</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> </tr> <tr style="height:20.4000pt; "> <td width="135" valign="center" style="width: 101.75pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">社会网络分析</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="154" valign="center" style="width: 115.7pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:17.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">网络图中有用信息</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="190" valign="center" style="width: 142.55pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">度、介数、亲密度等</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="88" valign="center" style="width: 66.25pt; padding: 0pt 5.4pt; border-top-width: 0.5pt; border-top-style: solid; border-top-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:10.0000pt; mso-line-height-rule:exactly; "><span class="15" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 9pt;">31-33</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> </tr> <tr style="height:19.2000pt; "> <td width="135" valign="center" style="width: 101.75pt; padding: 0pt 5.4pt; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">系统科学分析</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="154" valign="center" style="width: 115.7pt; padding: 0pt 5.4pt; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:17.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">节点破坏后的影响</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="190" valign="center" style="width: 142.55pt; padding: 0pt 5.4pt; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">核、核度等</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="88" valign="center" style="width: 66.25pt; padding: 0pt 5.4pt; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:10.0000pt; mso-line-height-rule:exactly; "><span class="15" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 9pt;">34</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> </tr> <tr style="height:21.1000pt; "> <td width="135" valign="center" style="width: 101.75pt; padding: 0pt 5.4pt; border-bottom-width: 0.5pt; border-bottom-style: solid; border-bottom-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">信息搜索分析</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="154" valign="center" style="width: 115.7pt; padding: 0pt 5.4pt; border-bottom-width: 0.5pt; border-bottom-style: solid; border-bottom-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:9.5000pt; mso-line-height-rule:exactly; "><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">节点间链接关系</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="190" valign="center" style="width: 142.55pt; padding: 0pt 5.4pt; border-bottom-width: 0.5pt; border-bottom-style: solid; border-bottom-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:10.0000pt; mso-line-height-rule:exactly; "><span class="15" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 9pt;">Leaderrank </span><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">法</span><span class="15" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 9pt;">、</span><span class="15" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 9pt;">Hits </span><span class="16" style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">法等</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> <td width="88" valign="center" style="width: 66.25pt; padding: 0pt 5.4pt; border-bottom-width: 0.5pt; border-bottom-style: solid; border-bottom-color: windowtext; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"> <p class="NewStyle18" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:0.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; line-height:10.0000pt; mso-line-height-rule:exactly; "><span class="15" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 9pt;">35-36</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"><o:p></o:p></span></p> </td> </tr> </tbody> </table> <p class="NewStyle20" style="margin: 0pt 0pt 0pt 8pt; text-indent: 24pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">文献</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[37]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">通过将网络图中的某一节点删除，然后计算生成树的数量，生成树 越少则代表节点重要度越高，但是如果若干个节点删除后都会使网络不连通， 就会导致此类节点的重要度相等而忽视了相邻节点的影响；文献</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[38]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">通过度中心 度来刻画节点重要度，度数越大能直接影响的邻居节点越多，重要度越大； </span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">Chen</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[39]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">等人提出了一种用半局部中心性来评价节点重要度的方法；</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">Kitsak</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">等人 </span><span class="19" style="font-family: 宋体; letter-spacing: -1pt; font-size: 9pt; vertical-align: super;">[4()]</span><span class="19" style="font-family: 宋体; letter-spacing: -1pt; font-size: 9pt;">提出了</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"> </span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">K</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">-</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">壳分解法，将外围节点逐步去掉，剩余的节点的重要度将会较高， 但是这种方法不适用于树形图、星型图或</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">BA</span><span class="19" style="font-family: 宋体; letter-spacing: -1pt; font-size: 9pt;">网络</span><span class="19" style="font-family: 宋体; letter-spacing: -1pt; font-size: 9pt; vertical-align: super;">[41]</span><span class="19" style="font-family: 宋体; letter-spacing: -1pt; font-size: 9pt;">;</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;"> </span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">Albert</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[42]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">提出利用离心 中心度作为指标衡量节点重要度，但这种方法容易受到某些特殊节点的影响； 特征向量中心性</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[43]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">不能反映相邻节点的数量，还能表征相邻节点本身的重要性; 文献</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[44]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">提出利用</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">Leademmk</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">算法的原理和计算方法，并将此算法运用到社会网 络节点重要度的计算上来；文献</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[45]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">提出</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">HITS</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">算法，给每个节点度量权威值和 枢纽值来度量节点重要性；还有其他</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9pt;">SALSA</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">算法</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[46]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">、节点收缩法</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[47]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">、自动信 息汇集算法</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt; vertical-align: super;">[48]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 9pt;">也被广泛应用于复杂网络的节点重要度求解问题。</span></p> <p class="MsoNormal"><span style="font-size:9.0pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">本文采摘自“基于故障率相关的加工中心的可靠性及风险评估”，因为编辑困难导致有些函数、表格、图片、内容无法显示，有需要者可以在网络中查找相关文章！</span><span lang="EN-US" style="font-size:9.0pt"><o:p></o:p></span></p> <p class="MsoNormal"><span style="font-size:9.0pt;font-family:宋体;mso-ascii-font-family: 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