Community Detection with and without Prior Information

Abstract

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.

6 pages, 2 figures

References in corpus (6)

• Modularity and community structure in networks
• Community detection in graphs
• Comparing community structure identification
• Statistical Mechanics of Community Detection
• (Un)detectable cluster structure in sparse networks
• Unsupervised and semi-supervised clustering by message passing: Soft-constraint affinity propagation

Cited by in corpus (7)

• Phase transitions in semisupervised clustering of sparse networks
• Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives
• Multi-resolution community detection based on generalized self-loop rescaling strategy
• Phase Transitions in Community Detection: A Solvable Toy Model
• Mean Field Analysis of Personalized PageRank with Implications for Local Graph Clustering
• Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs
• Stochastic fluctuations and the detectability limit of network communities