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2.3.7 Clustering coefficient The clustering coefficient of a node i, denoted by c(i), is defined as the number of directed links that exist between the node’s neighbors, divided by the number of possible directed links that could exist between the node’s neighbors. Thus, if a node i’s neighbors have n directed links between them, then the clustering coefficient of i is defined as c(i) = n (2.4) di(di − 1) The clustering coefficient of a graph is the average clustering coefficient of all its nodes, and we denote it as C(G), or C(G) = v∈V c(v) (2.5) |V| Thus, the clustering coefficient of a graph ranges between 0 and 1, with higher values representing a higher degree of “cliquishness” between the nodes. In particular, a graph with clustering coefficient of 0 contains no “triangles” of connected nodes, whereas a graph with clustering coefficient of 1 is a perfect clique. 2.3.8 Betweenness centrality The betweenness centrality B of an edge, originally proposed by Girvan and New- man [119], is defined as the number of shortest paths between all pairs of vertices in the graph that cross the edge. If a pair of vertices have multiple shortest paths between them, then each path is assigned a weight such that the sum over all paths 27PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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