Generalised power graph compression reveals dominant relationship patterns in complex networks

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.