Publication record · 18.cifr/2006.newman.spectral-modularity
18.cifr/2006.newman.spectral-modularityMany networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as modularity over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times.
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Recursive bisection may miss optimal multi-way partitions; direct k-way spectral methods using top-k eigenvectors of B are a natural extension. The resolution limit of modularity means small communities in large networks can be missed, motivating alternative quality functions.