The art of community detection

Abstract

SUMMARYNetworks in nature possess a remarkable amount of structure. Via a series of datadriven discoveries, the cutting edge of network science has recently progressed from positing that the random graphs of mathematical graph theory might accurately describe real networks to the current viewpoint that networks in nature are highly complex and structured entities. The identification of high order structures in networks unveils insights into their functional organization. Recently, Clauset, Moore, and Newman 1 , introduced a new algorithm that identifies such heterogeneities in complex networks by utilizing the hierarchy that necessarily organizes the many levels of structure. Here, we anchor their algorithm in a general community detection framework and discuss the future of community detection. STRUCTURE EVERYWHEREThe view that networks are essentially random was challenged in 1999 when it was discovered that the distribution of number of links per node (degree) of many real networks (internet, metabolic network, sexual contacts, airports, etc) is different from what is expected in random networks 2 . In a large random network node degrees are distributed according to the normal distribution, but in many manmade and biological networks the degree distribution follows a power-law. In the human protein-protein interaction networks 3,4 , for instance, some proteins act as hubs, they are highly connected, and interact with more than 200 other proteins contrary to most proteins that interact with only a few other proteins.Various local to global measures have been introduced to unveil the organizational principles of complex networks 5,6,7,8,9 . Maslov and Sneppen 10 discovered that who links to whom can depend on node degree; in many biological networks, high degree nodes systematically link to nodes of low degree. This disassortativity decreases the likelihood of cross talk between functional modules inside the cell and increases overall robustness. Other networks, for example social networks 11 , are highly assortative -in these networks nodes with similar degree tend to link to each other. The scales of organization of complex networks. The illustrations on the left show how to break down the "hairball" that arises when we plot the entire network. On the smallest scale, the degree provides information about single nodes. The notion of assortativity enters when we discuss pairs of nodes. With three or more nodes, we are in the realm of motifs. Larger groups of nodes are called modules or communities. Hierarchy describes how the various structural elements are combined; how nodes a linked to form motifs, motifs are combined to form communities, and communities are joined into the entire network.Going beyond the properties of single nodes and pairs of nodes, the natural next step is to consider structures that include several nodes. Interestingly, a few select motifs of three to four nodes are ubiquitous in real networks 12 while most others occur only as often as they would at random, or, are actively suppressed....

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“…The heterogeneous distribution of the links has led to community structure [10][11][12]. A community is a set of entities which are linked to all the other entities in the network.…”

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