By Hua-Wei Shen (auth.)
Community constitution is a salient structural attribute of many real-world networks. groups are as a rule hierarchical, overlapping, multi-scale and coexist with different varieties of structural regularities of networks. This poses significant demanding situations for traditional tools of group detection. This e-book will comprehensively introduce the most recent advances in group detection, particularly the detection of overlapping and hierarchical group constructions, the detection of multi-scale groups in heterogeneous networks, and the exploration of a number of varieties of structural regularities. those advances were effectively utilized to research large-scale on-line social networks, akin to fb and Twitter. This e-book offers readers a handy strategy to clutch the innovative of group detection in complicated networks.
The thesis on which this e-book is predicated used to be venerated with the “Top a hundred very good Doctoral Dissertations Award” from the chinese language Academy of Sciences and used to be nominated because the “Outstanding Doctoral Dissertation” by means of the chinese language machine Federation.
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Additional info for Community Structure of Complex Networks
The label of each leaf node shows the nodes belonging to it. The (red) vertical dashed line is a cut through the dendrogram and it gives the best cover of the network. The top part of the figure is a graph which illustrates the curve of EQ corresponding to each cover of the network. The threshold k is set to be 4. Reprinted from Ref. , Copyright 2009, with permission from Elsevier Similar to the fast algorithm in , the process of our algorithm corresponds to a dendrogram, which shows the order of the amalgamations of communities.
3, δvc denotes whether the node v belongs to the community c. The value of δvc is 1 when the node v belongs to the community c and 0 otherwise. For a cover of network, however, a node may belong to more than one community. Thus δvc needs to be extended to a belonging coefficient αvc , which reflects how much the node v belongs to the community c. With the belonging coefficient αvc , the goodness of a cover C can be measured by Qc = 1 L αvc αwc Avw − c∈C vw kv kw . 4) The idea of the belonging coefficient was proposed in .
Communities are differentiated by colors and the overlapping regions are emphasized in red. The edges between communities are colored in gray. Reprinted from Ref. 3 Extending Modularity to Quantify the Overlapping Community Structure 31 where A is the adjacency matrix of the network G, L = vw Avw is the total weight of all the edges, and kv = w Avw is the degree of the node v. In Eq. 3, δvc denotes whether the node v belongs to the community c. The value of δvc is 1 when the node v belongs to the community c and 0 otherwise.