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===Centrality measures===

===Centrality measures===

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"/>

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"/>

*'''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.

*'''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.

*'''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.

*'''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>

*'''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>