Spectral tripartitioning of networks

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.

12 pages with 4 figures, resubmitted version accepted for publication in Physical Review E

References in corpus (9)

• Fast unfolding of communities in large networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Comparing community structure identification
• Hierarchical structure and the prediction of missing links in networks
• Detecting the overlapping and hierarchical community structure of complex networks
• Quantifying social group evolution
• Community structure in directed networks
• Analysis of the structure of complex networks at different resolution levels
• A Bayesian Approach to Network Modularity