While there exist a wide range of effective methods for community detection in networks, most of them require one to know in advance how many communities one is looking for. Here we present a method for estimating the number of communities in a network using a combination of Bayesian inference with a novel prior and an efficient Monte Carlo sampling scheme. We test the method extensively on both real and computer-generated networks, showing that it performs accurately and consistently, even in cases where groups are widely varying in size or structure.

 

Efficient method for estimating the number of communities in a network
Maria A. Riolo, George T. Cantwell, Gesine Reinert, M. E. J. Newman

Source: arxiv.org

We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual, highly modular networks. Individual network realizations typically contain multiple macrohubs—nodes whose degree scales linearly with the number of nodes N. The size of the network “nucleus”—the set of nodes of degree greater than one—grows sublinearly with N and thus constitutes a vanishingly small fraction of the network. The network therefore consists almost entirely of leaves (nodes of degree one) as N→∞.

 

Emergent Network Modularity
P. L. Krapivsky, S. Redner

Source: arxiv.org

New math shows how, contrary to conventional scientific wisdom, conscious beings and other macroscopic entities might have greater influence over the future than does the sum of their microscopic components.

Source: www.quantamagazine.org