Abstract
We introduce a framework for the discovery of dominant relationship patterns in complex networks, by compressing the networks into power graphs with overlapping power nodes. When paired with enrichment analysis of node classification terms, the most compressible sets of edges provide a highly informative sketch of the dominant relationship patterns that define the network. In addition, this procedure also gives rise to a novel, link-based definition of overlapping node communities in which nodes are defined by their relationships with sets of other nodes, rather than through connections within the community. We show that this completely general approach can be applied to undirected, directed, and bipartite networks, yielding valuable insights into the large-scale structure of real-world networks, including social networks and food webs. Our approach therefore provides a novel way in which network architecture can be studied, defined and classified.
Highlights
Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
We introduce a framework for the discovery of dominant relationship patterns in complex networks, by compressing the networks into power graphs with overlapping power nodes
A method for detecting bicliques might have picked up the result found in the ingredient-recipe network, but such methods are tailored to bipartite networks, whereas compressible components can be applied to any network, whether it happens to be bipartite or not
Summary
Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom. When paired with enrichment analysis of node classification terms, the most compressible sets of edges provide a highly informative sketch of the dominant relationship patterns that define the network This procedure gives rise to a novel, link-based definition of overlapping node communities in which nodes are defined by their relationships with sets of other nodes, rather than through connections within the community. Our aim is to transcend these definitions by proposing a completely general way of identifying dominant relationship structures in networks through lossless compression of networks into power graphs This approach places no constraints on the overlap between sets of nodes. The information required to specify all nAnB edges that connect the nA nodes in A with the nB nodes in B is: IAB~2nAnB log[2] N ð2Þ
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