%0 Journal Article %1 richardson_spectral_2009 %A Richardson, Thomas %A Mucha, Peter J. %A Porter, Mason A. %D 2009 %J Physical Review E %K analysis, community detection, eigenvalue, modularity, network spectral %N 3 %P 036111 %R 10.1103/PhysRevE.80.036111 %T Spectral tripartitioning of networks %U http://link.aps.org/doi/10.1103/PhysRevE.80.036111 %V 80 %X 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 M. E. J. Newman Proc. Natl. Acad. Sci. U.S.A. 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.

@article{richardson_spectral_2009, 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 [ M. E. J. Newman Proc. Natl. Acad. Sci. U.S.A. 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.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Richardson, Thomas and Mucha, Peter J. and Porter, Mason A.}, biburl = {https://www.bibsonomy.org/bibtex/2d7aa9fc67f3c3c34cc0fcb1ae3355747/yourwelcome}, doi = {10.1103/PhysRevE.80.036111}, interhash = {4f46b143cf6c1a6b7f3df87e4c8cacbb}, intrahash = {d7aa9fc67f3c3c34cc0fcb1ae3355747}, journal = {Physical Review E}, keywords = {analysis, community detection, eigenvalue, modularity, network spectral}, month = sep, number = 3, pages = 036111, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Spectral tripartitioning of networks}, url = {http://link.aps.org/doi/10.1103/PhysRevE.80.036111}, urldate = {2013-11-17}, volume = 80, year = 2009 }