Download Community Structure of Complex Networks by Hua-Wei Shen (auth.) PDF

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 kinds of structural regularities of networks. This poses significant demanding situations for traditional equipment of group detection. This booklet will comprehensively introduce the newest advances in group detection, particularly the detection of overlapping and hierarchical group buildings, the detection of multi-scale groups in heterogeneous networks, and the exploration of a number of sorts of structural regularities. those advances were effectively utilized to research large-scale on-line social networks, akin to fb and Twitter. This booklet offers readers a handy solution to seize the innovative of group detection in advanced networks.
The thesis on which this e-book is predicated was once commemorated with the “Top a hundred very good Doctoral Dissertations Award” from the chinese language Academy of Sciences and was once nominated because the “Outstanding Doctoral Dissertation” through the chinese language desktop Federation.

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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. 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.

The maximal cliques, whose nodes are from some other larger maximal cliques, are called subordinate maximal cliques. For example, in Fig. 1, nodes 4 and 23 form a subordinate maximal clique. Because node 4 is from another larger maximal clique {1, 2, 3, 4, 5, 6} and node 23 is also from other larger maximal cliques, including {18, 20, 21, 23}, {18, 20, 22, 23} and {18, 19, 22, 23}. Subordinate maximal cliques may mislead our algorithm and thus are discarded. Most subordinate maximal cliques have small sizes.

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