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===中心性度量===

===中心性度量===

Information about the relative importance of nodes and edges in a graph can be obtained through [[centrality]] measures, widely used in disciplines like [[sociology]]. Centrality measures are essential when a network analysis has to answer questions such as: "Which nodes in the network should be targeted to ensure that a message or information spreads to all or most nodes in the network?" or conversely, "Which nodes should be targeted to curtail the spread of a disease?". Formally established measures of centrality are [[degree centrality]], [[closeness centrality]], [[betweenness centrality]], [[eigenvector centrality]], and [[katz centrality]]. The objective of network analysis generally determines the type of centrality measure(s) to be used.<ref name="Wasserman_Faust"/>

关于图中节点和边的相对重要性的信息可以通过[[中心性]]度量来获得，[[中心性]]在[[社会学]]等学科广泛使用。当网络分析必须回答下面问题时，中心性度量必不可少:“为了确保消息或信息传播到网络中的全部或大部分节点，网络中哪些节点应该特别关注?”或相反地,“应该控制哪些节点以限制疾病的传播?”。正式确立的中心性度量有[[度中心性]]、[[紧密中心性]]、[[中介中心性]]、[[本征向量中心性]]和[[Katz中心性]]。网络分析的目标一般地决定了所使用的中心性度量的类型。<ref name="Wasserman_Faust"/>

*'''Degree centrality''' of a node in a network is the number of links (vertices) incident on the node.

*'''Degree centrality''' of a node in a network is the number of links (vertices) incident on the node.

*'''度中心性'''是指网络中节点的

*'''度中心性'''是指网络中与某节点相关联的连接（节点）数。

*'''Closeness centrality''' determines how "close" a node is to other nodes in a network by measuring the sum of the shortest distances (geodesic paths) between that node and all other nodes in the network.

*'''紧密中心性'''决定了网络中一个节点和其他节点的“紧密”程度，通过计算该节点和网络中其他节点最短路径的和来度量。

*'''Betweenness centrality''' determines the relative importance of a node by measuring the amount of traffic flowing through that node to other nodes in the network. This is done by measuring the fraction of paths connecting all pairs of nodes and containing the node of interest. Group Betweenness centrality measures the amount of traffic flowing through a group of nodes.<ref>{{cite journal | last1 = Puzis | first1 = R. | last2 = Yagil | first2 = D. | last3 = Elovici | first3 = Y. | last4 = Braha | first4 = D. | year = 2009 | title = Collaborative attack on Internet users' anonymity | url = http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf | journal = Internet Research | volume = 19 | issue =  | page = 1 | doi = 10.1108/10662240910927821 | citeseerx = 10.1.1.219.3949 | access-date = 2015-02-08 | archive-url = https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf | archive-date = 2013-12-07 | url-status = dead }}</ref>

*'''中介中心性''' 通过计算通过某节点到网络中其他节点的流量来确定该节点的相对重要性。determines the relative importance of a node by measuring the amount of traffic flowing through that node to other nodes in the network. This is done by measuring the fraction of paths connecting all pairs of nodes and containing the node of interest. Group Betweenness centrality measures the amount of traffic flowing through a group of nodes.<ref>{{cite journal | last1 = Puzis | first1 = R. | last2 = Yagil | first2 = D. | last3 = Elovici | first3 = Y. | last4 = Braha | first4 = D. | year = 2009 | title = Collaborative attack on Internet users' anonymity | url = http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf | journal = Internet Research | volume = 19 | issue =  | page = 1 | doi = 10.1108/10662240910927821 | citeseerx = 10.1.1.219.3949 | access-date = 2015-02-08 | archive-url = https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf | archive-date = 2013-12-07 | url-status = dead }}</ref>

*'''Eigenvector centrality''' is a more sophisticated version of degree centrality where the centrality of a node not only depends on the number of links incident on the node but also the quality of those links. This quality factor is determined by the eigenvectors of the adjacency matrix of the network.

*'''Eigenvector centrality''' is a more sophisticated version of degree centrality where the centrality of a node not only depends on the number of links incident on the node but also the quality of those links. This quality factor is determined by the eigenvectors of the adjacency matrix of the network.

*'''Katz centrality''' of a node is measured by summing the geodesic paths between that node and all (reachable) nodes in the network.  These paths are weighted, paths connecting the node with its immediate neighbors carry higher weights than those which connect with nodes farther away from the immediate neighbors.

*'''Katz centrality''' of a node is measured by summing the geodesic paths between that node and all (reachable) nodes in the network.  These paths are weighted, paths connecting the node with its immediate neighbors carry higher weights than those which connect with nodes farther away from the immediate neighbors.