Statistical test for detecting community structure in real-valued   edge-weighted graphs
  We propose a novel method to test the existence of community structure of undirected real-valued edge-weighted graph. The method is based on Wigner semicircular law on the asymptotic behavior of the random distribution for eigenvalues of a real symmetric matrix. We provide a theoretical foundation for this method and report on its performance in synthetic and real data, suggesting that our method outperforms other state-of-the-art methods. 
Tomoki Tokuda
math.ST cs.SI physics.soc-ph stat.TH