Structural Regularity Exploring and Controlling: A Network Reconstruction Perspective
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The ubiquitous complex networks are often composed of regular and irregular components, which makes uncovering the complexity of network structure into a fundamental challenge in network science. Exploring the regular information and identifying the roles of microscopic elements in network organization can help practitioners to recognize the universal principles of network formation and facilitate network data mining.Despite many algorithms having been proposed for link prediction and network reconstruction, estimating and regulating the reconstructability of complex networks remains an inadequately explored problem. With the practical assumption that there has consistence between local structures of networks and the corresponding adjacency matrices are approximately low rank, we obtain a self-representation network model in which the organization principles of networks are captured by representation matrix. According to the model, original networks can be reconstructed based on observed structure. What's more, the model enables us to estimate to what extent networks are regulable, in other words, measure the reconstructability of complex networks. In addition, the model enables us to measure the importance of network links for network regularity thereby allowing us to regulate the reconstructability of networks. The extensive experiments on disparate networks demonstrate the effectiveness of the proposed algorithm and measure. Specifically, the structural regularity reflects the reconstructability of networks, and the reconstruction accuracy can be promoted via the deleting of irregular network links independent of specific algorithms.
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