Community structure from spectral properties in complex networks

Weanalyze the spectral properties of complex networks focusing on theirrelation to the community structure, and develop an algorithm basedon correlations among components of different eigenvectors. The algorithm appliesto general weighted networks, and, in a suitably modified version,to the case of directed networks. Our method allows tocorrectly detect communities in sharply partitioned graphs, however it isuseful to the analysis of more complex networks, without awell defined cluster structure, as social and information networks. Asan example, we test the algorithm on a large scaledata-set from a psychological experiment of free word association, whereit proves to be successful both in clustering words, andin uncovering mental association patterns. ©2005 American Institute of Physics