Network Reconstruction and Controlling Based on Structural Regularity Analysis

From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular information and identifying the roles of microscopic elements in network data can help us recognize the principle of network organization and contribute to network data utilization. However, the intrinsic structural properties of networks remain so far inadequately explored and theorised. With the realistic assumption that there are consistent features across the local structures of networks, we propose a low-rank pursuit based self-representation network model, in which the principle of network organization can be uncovered by a representation matrix. According to this model, original true networks can be reconstructed based on the observed unreliable network topology. In particular, the proposed model enables us to estimate the extent to which the networks are regulable, i.e., measuring the reconstructability of networks. In addition, the model is capable of measuring the importance of microscopic network elements, i.e., nodes and links, in terms of network regularity thereby allowing us to regulate the reconstructability of networks based on them. Extensive experiments on disparate real-world networks demonstrate the effectiveness of the proposed network reconstruction and regulation algorithm. Specifically, the network regularity metric can reflect the reconstructability of networks, and the reconstruction accuracy can be improved by removing irregular network links. Lastly, our approach provides an unique and novel insight into the organization exploring of complex networks.