Spectral tripartitioning of networks

Details Spectral tripartitioning of networks Spectral tripartitioning of networks

2008-12-15

arxiv.org/abs/0812.2852v2

Physical Review E vol.80 036111 (2009)

Physics

Data Analysis, Statistics and Probability

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

Scientific paper

10.1103/PhysRevE.80.036111

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.

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