Community Detection with and without Prior Information

Details Community Detection with and without Prior Information Community Detection with and without Prior Information

2009-07-27

arxiv.org/abs/0907.4803v2

Europhysics Letters 90, p.18002, 2010

Physics

Physics and Society

6 pages, 2 figures

Scientific paper

10.1209/0295-5075/90/18002

We study the problem of graph partitioning, or clustering, in sparse networks with prior information about the clusters. Specifically, we assume that for a fraction $\rho$ of the nodes their true cluster assignments are known in advance. This can be understood as a semi--supervised version of clustering, in contrast to unsupervised clustering where the only available information is the graph structure. In the unsupervised case, it is known that there is a threshold of the inter--cluster connectivity beyond which clusters cannot be detected. Here we study the impact of the prior information on the detection threshold, and show that even minute [but generic] values of $\rho>0$ shift the threshold downwards to its lowest possible value. For weighted graphs we show that a small semi--supervising can be used for a non-trivial definition of communities.

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