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Multilayer networks are in the focus of the current complex network study. Insuch networks multiple types of links may exist as well as many attributes fornodes. To fully use multilayer -- and other types of complex networks inapplications, the merging of various data with topological information rendersa powerful analysis. First, we suggest a simple way of representing networkdata in a data matrix where rows correspond to the nodes, and columnscorrespond to the data items. The number of columns is allowed to be arbitrary,so that the data matrix can be easily expanded by adding columns. The datamatrix can be chosen according to targets of the analysis, and may vary a lotfrom case to case. Next, we partition the rows of the data matrix intocommunities using a method which allows maximal compression of the data matrix.For compressing a data matrix, we suggest to extend so called regulardecomposition method for non-square matrices. We illustrate our method forseveral types of data matrices, in particular, distance matrices, and matricesobtained by augmenting a distance matrix by a column of node degrees, or byconcatenating several distances matrices corresponding to layers of amultilayer network. We illustrate our method with synthetic power-law graphsand two real networks: an Internet autonomous systems graph and a world airlinegraph. We compare the outputs of different community recovery methods on thesegraphs, and discuss how incorporating node degrees as a separate column to thedata matrix leads our method to identify community structures well-aligned withtiered hierarchical structures commonly encountered in complex scale-freenetworks.

A network community detection method with integration of data from multiple layers and node attributes