Abstract
We propose a novel method to test the existence of community structure in undirected, real-valued, edge-weighted graphs. The method is based on the asymptotic behavior of extreme eigenvalues of a real symmetric edge-weight matrix. We provide a theoretical foundation for this method and report on its performance using synthetic and real data, suggesting that this new method outperforms other state-of-the-art methods.
Highlights
Clustering objects based on their similarities is a basic data mining approach in statistical analysis
We propose a general method for testing community structure of edge-weighted graphs with real-valued weights, which does not require a cluster solution
In regard to statistical power, it is implied that our method can readily detect the existence of community structure when means μk,k0 in each block differ by at most 0.3 (3 × 0.05 + 3 × 0.05) when σk,k0 = 1 with the number of nodes being 750 (Fig 4B)
Summary
Clustering objects based on their similarities is a basic data mining approach in statistical analysis. To detect such structure, a number of clustering methods have been proposed in the statistical physics and information theory literature [2,3,4]. The conventional framework for analysis of community structure is typically an unsigned graph in which an edge weight is constrained to be non-negative. How to cluster nodes in a more general framework, such as negative edge weights within a cluster, remains an open question [7]
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