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2.3.5 Scale-free behavior The scale-free metric s(G) [91] of a graph is a value calculated directly from the joint degree distribution of a graph. The scale-free metric ranges between 0 and 1, and measures the extent to which the graph has a hub-like core. To define the s(G), we first define s′(G) as s′(G) = didj (i,j )∈E Then, we define the scale-free metric s(G) as s′ (G) distribution of G. A high scale-free metric means that high-degree nodes tend to connect to other high-degree nodes, while a low scale-free metric means that high- degree nodes tend to connect to low-degree nodes. 2.3.6 Assortativity The scale-free metric is related to the assortativity coefficient r, which is a measure of the likelihood for nodes to connect to other nodes with similar degrees. The assortativity is defined as the Pearson correlation coefficient between the degrees of all pairs of nodes connected by an edge. Thus, the assortativity coefficient ranges between -1 and 1; a high assortativity coefficient means that nodes tend to connect to nodes of similar degree, while a negative coefficient means that nodes likely connect to nodes with very different degree from their own. (2.3) where s′ represents the maximum value of s′ over all graphs with the same degree s(G) = s′ max (2.2) 26 maxPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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