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• W1985339741 abstract "Community structure plays a significant role in the analysis of social networks and similar graphs, yet this structure is little understood and not well captured by most models. We formally define a community to be a subgraph that is internally highly connected and has no deeper substructure. We use tools of combinatorics to show that any such community must contain a dense Erdos-R'enyi (ER) subgraph. Based on mathematical arguments, we hypothesize that any graph with a heavy-tailed degree distribution and community structure must contain a scale free collection of dense ER subgraphs. These theoretical observations corroborate well with empirical evidence. From this, we propose the Block Two-Level Erdos-R'enyi (BTER) model, and demonstrate that it accurately captures the observable properties of many real-world social networks." @default.
• W1985339741 created "2016-06-24" @default.
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• W1985339741 date "2012-05-10" @default.
• W1985339741 modified "2023-10-02" @default.
• W1985339741 title "Community structure and scale-free collections of Erdős-Rényi graphs" @default.
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• W1985339741 doi "https://doi.org/10.1103/physreve.85.056109" @default.
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