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nature_Uncovering the overlapping community structure of complex networks in nature and society.pdf

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nature_Uncovering the overlapping community structure of complex networks in nature and society

Uncovering the overlapping community structure of complex networks in nature and society Gergely Palla1,2, Imre Dere?nyi2, Ille?s Farkas1 Tama?s Vicsek1,2 Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of1–4. A key question is how to interpret the global organization of such networks as the co- existence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins5,6, industrial sectors7 and groups of people8,9) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large net- works find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping commu- nities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties. Most real networks typically contain parts in which the nodes (units) are more highly connected to each other than to the rest of the network. The sets of such nodes are usually called clusters, communities, cohesive groups or modules8,10,11–13; they have no widely accepted, unique definition. In spite of this ambiguity, the presence of communities in networks is a signature of the hierarchical nature of complex