Spanning tree separation reveals community structure in networks

Abstract

We present a simple, intuitive, and effective approach for network clustering. It is based on basic concepts of linear algebra such as efficient calculation of spanning trees, and can be implemented in a few lines of code. We introduce the node separation measure spanning tree separation (STS) and the corresponding graph distance measure spanning tree vector similarity distance (STVSD). We demonstrate that the STS is a link salience measure able to identify the backbone of networks. The STVSD is used to reveal the hierarchical community structure of networks. We show that it, together with the clustering quality measure partition density, is on a par with the best graph or network clustering methods known, in terms of both quality and efficiency. In perspective, we note that our approach could also handle weighted and directed networks and could be used for identification of overlapping communities.