  Multilayer networks are in the focus of the current complex network study. In
such networks multiple types of links may exist as well as many attributes for
nodes. To fully use multilayer -- and other types of complex networks in
applications, the merging of various data with topological information renders
a powerful analysis. First, we suggest a simple way of representing network
data in a data matrix where rows correspond to the nodes, and columns
correspond 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 data
matrix can be chosen according to targets of the analysis, and may vary a lot
from case to case. Next, we partition the rows of the data matrix into
communities using a method which allows maximal compression of the data matrix.
For compressing a data matrix, we suggest to extend so called regular
decomposition method for non-square matrices. We illustrate our method for
several types of data matrices, in particular, distance matrices, and matrices
obtained by augmenting a distance matrix by a column of node degrees, or by
concatenating several distances matrices corresponding to layers of a
multilayer network. We illustrate our method with synthetic power-law graphs
and two real networks: an Internet autonomous systems graph and a world airline
graph. We compare the outputs of different community recovery methods on these
graphs, and discuss how incorporating node degrees as a separate column to the
data matrix leads our method to identify community structures well-aligned with
tiered hierarchical structures commonly encountered in complex scale-free
networks.
