网络的谱三分法
Spectral tripartitioning of networks
摘要：
我们制定了一个谱图分割算法，使用对应于选定的质量函数的矩阵的两个领先的特征向量分裂成三个社区的网络在一个单一的步骤。在这样做时，我们扩展了递归bipartitioning方法开发的纽曼[Proc. Nat. Sci. 103，8577（2006）; Phys.Rev.E74，036104（2006）]，以允许在每个递归步骤考虑最佳可用的双向和三向划分。我们使用简单的“水桶旅”的例子来说明该方法，然后应用该算法来检查网络科学家和U。S.国会网络从唱名投票的相似性推断。
英文摘要：
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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