Core–periphery structure is an essential mesoscale feature in complex networks. Previous researches mostly focus on discriminative approaches, while in this work we propose a generative model called masked Bayesian nonnegative matrix factorization. We build the model using two pair affiliation matrices to indicate core–periphery pair associations and using a mask matrix to highlight connections to core nodes. We propose an approach to infer the model parameters and prove the convergence of variables with our approach. Besides the abilities as traditional approaches, it is able to identify core scores with overlapping core–periphery pairs. We verify the effectiveness of our method using randomly generated networks and real-world networks. Experimental results demonstrate that the proposed method outperforms traditional approaches.

Graph neural networks (GNNs) are powerful models for processing graph data and have demonstrated state-of-the-art performance on many downstream tasks. However, existing GNNs can generally suffer from two limitations: over-smoothing and over-squashing, which can significantly undermine their learning ability for large graphs. To overcome these issues simultaneously, by utilizing the concept of effective resistances, we focus on minimizing total constrained resistance while identifying problematic edges using topological redundancy and bottleneck sparsity coefficients. We introduce a novel graph rewiring and preprocessing method guided by effective resistance (GPER), capable of edge addition or removal. Theoretical analysis validates our method's efficacy in mitigating over-smoothing and over-squashing. In the experiments, we conduct node and graph classifications on the benchmark datasets and can achieve an average improvement of 7.8% and 2.0%, respectively. We also conduct scalability analysis on large graphs with GCN and demonstrate that the proposed preprocess approach can reduce graph size by over 50% while improve the performance.