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.

翻译：多层网络是当前复杂网络研究的焦点。此类网络中可能存在多种类型的连接以及丰富的节点属性。为了在应用中充分利用多层网络及其他复杂网络结构，将多源数据与拓扑信息相融合能带来强大的分析能力。首先，我们提出一种简单的网络数据表示方法，将数据组织为矩阵形式：行对应节点，列对应数据项。列数可任意扩展，从而便于通过添加新列扩充数据矩阵。该数据矩阵可根据分析目标灵活选取，且在不同场景下差异显著。其次，我们采用一种能对数据矩阵进行最大压缩的方法，将矩阵行划分为社区。为实现数据矩阵压缩，我们建议将常规的"正则分解方法"扩展至非方阵场景。我们针对多种类型的数据矩阵展示了该方法的有效性，包括：距离矩阵、通过向距离矩阵添加节点度数列得到的矩阵，以及拼接多层网络中各层对应的多个距离矩阵形成的矩阵。通过合成无标度图及两个真实网络（互联网自治系统图和全球航线图）进行验证，我们比较了不同社区发现方法在这些图上的输出结果，并讨论了将节点度数作为独立列引入数据矩阵后，如何使我们的方法识别出与复杂无标度网络中常见的分层结构高度一致的社区结构。