Detecting community structure and structural hole spanner simultaneously by using graph convolutional network based Auto-Encoder

Abstract

Both Community and Structural Hole (SH) Spanner Detection are significant research tasks in social network analysis. Due to the close topological relevance between communities and structure hole spanners, the two tasks can work out synchronously, but most studies address the two tasks independently. In recent years, deep learning has been applied in the field of community detection. However, so far no deep learning model can solve both community and SH detection at the same framework. In this paper, we first analyze why a previous model named Harmony Modularity (HAM) can working for joint community and SH spanners detection task, which is the only one previous work that solve two task synchronously. Then we discuss the deficiency of HAM. For purpose of overcoming the shortcoming of HAM, we propose a deep learning model for finding both communities and structural holes simultaneously. Because the main framework used in our model is graph convolutional neural network based Auto-Encoder, we shorten it for ComSHAE. Specifically, ComSHAE learn the eigenvectors of weighted Spectral Ratio-Cut Partitioning and the nonlinear representation of adjacent matrix. We infer the community assignments and top-k SH spanners from eigenvectors. Extensive experimental results on synthetic and real networks show that our model outperform the baseline HAM and some state-of-the-art methods. When compare ComSHAE with HAM on synthetic data, ComSHAE shows great effects but HAM can not work. We use Normalized Mutual Information (NMI) to measure performance on detecting communites. ComSHAE shows abort 0.05 NMI improvement than HAM on real data and abort 0.63 NMI improvement on synthetic data. We measure the cross-community transmission capacity through structural hole influence index (SHII). The SH spanners found by ComSHAE shows at lest 0.03 SHII improvement compared with SH detection methods.