Spectral tripartitioning of networks

TL;DR

This paper introduces a spectral tripartitioning algorithm for networks that efficiently identifies three communities simultaneously using eigenvector analysis, extending previous bipartitioning methods for improved community detection.

Contribution

It extends spectral graph-partitioning to allow for three-way splits at each step, enabling more effective community detection in complex networks.

Findings

Successfully applied to coauthorship and Congressional networks

Identifies community structures more effectively than bipartitioning methods

Demonstrates the method's utility with simple and real-world examples

Abstract

We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [Proc. Nat. Acad. Sci. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow one to consider the best available two-way and three-way divisions at each recursive step. We illustrate the method using simple "bucket brigade" examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of U. S. Congressional networks inferred from roll-call voting similarities.