Network Summarization with Preserved Spectral Properties

Large-scale networks are widely used to represent object relationships in many real world applications. The occurrence of large-scale networks presents significant computational challenges to process, analyze, and extract information from such networks. Network summarization techniques are commonly used to reduce the computational load while attempting to maintain the basic structural properties of the original network. Previous works have primarily focused on some type of network partitioning strategies with application-dependent regularizations, most often resulting in strongly connected clusters. In this paper, we introduce a novel perspective regarding the network summarization problem based on concepts from spectral graph theory. We propose a new distance measurement to characterize the spectral differences between the original and coarsened networks. We rigorously justify the spectral distance with the interlacing theorem as well the results from the stochastic block model. We provide an efficient algorithm to generate the coarsened networks that maximally preserves the spectral properties of the original network. Our proposed network summarization framework allows the flexibility to generate a set of coarsened networks with significantly different structures preserved from different aspects of the original network, which distinguishes our work from others. We conduct extensive experimental tests on a variety of large-scale networks, both from real-world applications and the random graph model. We show that our proposed algorithms consistently perform better results in terms of the spectral measurements and running time compared to previous network summarization algorithms.