A community detection algorithm based on spectral co-clustering and weight self-adjustment in attributed stochastic co-block models

The Degree-Corrected Stochastic co-Block Model (DC-ScBM) is widely utilized for detecting the community structure in directed networks. It can flexibly depict the topology of edges in directed graphs. However, in practice, node attributes provide an additional source of information that can be leveraged for community detection, which is not considered in the DC-ScBM. Therefore, there is a critical need to develop models and detection methods for node-attributed directed networks, especially when the goal is to discover important nodes or special community structures. We generalize the DC-ScBM using the multiplicative form to fuse edges and node attributes and describe the extent of influence of node attributes on each community. Then, a detection algorithm based on spectral co-clustering and feature weight self-adjustment (Spcc-SA) is developed. The algorithm aims to minimize normalized cut (Ncut), and iteratively detects the sending and receiving communities and the weights of node attributes, so that node attributes with stronger signals are given greater weights. Numerical studies demonstrate that the Spcc-SA algorithm outperforms existing methods across a variety of node attributes and network topologies. Especially when attribute values differ greatly and the community structure is distinct, the normalized mutual information of Spcc-SA in the sending and receiving communities can reach 0.6 and 0.8, respectively. Furthermore, We apply this algorithm to real world datasets, including the Enron email, world trade, and Weddell Sea network, demonstrating that the algorithm can effectively detect interesting community structures.