To detect communities in complex networks, we generalize the modularity density(D) to weighted variants and show how optimizing the weighted function(WD) can be formulated as a spectral clustering problem, as well as a weighted kernel k-means clustering problem. We also prove equivalence of the both clustering approaches based on WD in mathematics. Using the equivalence, we propose a new eigenvector-based kernel clustering algorithms to detecting communities in complex networks, called two-layer approach.Experimental results indicate that it have better performance comparing with either direct kernel &-means algorithm or direct spectral clustering algorithm in term of quality.
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