Community Detection in Partial Correlation Network Models

Abstract

Many real-world networks exhibit a community structure: The vertices of the network are partitioned into groups such that the concentration of linkages is high among vertices in the same group and low otherwise. This motivates us to introduce a class of Gaussian graphical models with a community structure that replicates this empirical regularity. A natural question that arises in this framework is how to detect the communities from a random sample of observations. We introduce an algorithm called Blockbuster that recovers the communities using the eigenvectors of the sample covariance matrix. We study the properties of the procedure and establish consistency. The methodology is used to study real activity clustering in the U.S. and Europe.