Line graphs as social networks

Abstract

The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.

11 pages, 4 figures

References in corpus (7)

• Community detection in graphs
• Identification of influential spreaders in complex networks
• Line Graphs, Link Partitions and Overlapping Communities
• Two complementary representations of a scale-free network
• Clustering in random line graphs
• Clustering under the line graph transformation: Application to reaction network
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Cited by in corpus (5)

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• Fragmentation transition in a coevolving network with link-state dynamics
• Dynamics of link states in complex networks: The case of a majority rule
• Opinion formation in an open system and the spiral of silence
• Language dynamics within adaptive networks: An agent-based approach of nodes and links coevolution