Multilayer network community detection based on triangular motif and attribute information

Abstract Multilayer networks have emerged as a powerful framework for modeling the interrelationships among entities in complex systems. Existing research has shown that higher-order structures and node attributes can significantly enhance complex networks’ representational capacity. While higher-order structures focus on the connections between sets of nodes, rather than just pairwise connections, node attributes capture information beyond the network’s structural aspects. In this work, we develop an accurate and scalable method for community detection in higher-order multilayer networks with node attributes. The proposed method integrates three key aspects of multilayer networks: triangular motifs, pairwise links, and node attributes, to more effectively represent the observed interactions and outperform methods that rely solely on any one of these information sources. To achieve this, we construct an augmented proximity matrix as a linear combination of similarity matrices derived from these three aspects. To further account for the varying contributions of different attributes in community detection, the node attribute similarity matrix is formulated as a weighted sum of individual attribute similarity matrices. We employ an iterative spectral clustering algorithm to identify community structures and assess the differential contributions of various attributes within these communities. Our method demonstrates significant competitive advantages over existing approaches, as validated through experiments on real-world datasets and simulation studies.