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As a classical problem in the field of complex networks, link prediction has attracted much attention from researchers, which is of great significance to help us understand the evolution and dynamic development mechanisms of networks. Although various network type-specific algorithms have been proposed to tackle the link prediction problem, most of them suppose that the network structure is dominated by the Triadic Closure Principle. We still lack an adaptive and comprehensive understanding of network formation patterns for predicting potential links. In addition, it is valuable to investigate how network local information can be better utilized. To this end, we proposed a novel method named Link prediction using Multiple Order Local Information (MOLI) that exploits the local information from the neighbors of different distances, with parameters that can be a prior-driven based on prior knowledge, or data-driven by solving an optimization problem on observed networks. MOLI defined a local network diffusion process via random walks on the graph, resulting in better use of network information. We show that MOLI outperforms the other 11 widely used link prediction algorithms on 11 different types of simulated and real-world networks. We also conclude that there are different patterns of local information utilization for different networks, including social networks, communication networks, biological networks, etc. In particular, the classical common neighbor-based algorithm is not as adaptable to all social networks as it is perceived to be; instead, some of the social networks obey the Quadrilateral Closure Principle which preferentially connects paths of length three., Comment: 21 pages, 3 figures, 18 tables, and 29 references

Networks are widely used in many fields for their powerful ability to provide vivid representations of relationships between variables. However, many of them may be corrupted by experimental noise or inappropriate network inference methods that inherently hamper the efficacy of network-based downstream analysis. Consequently, it's necessary to develop systematic methods for denoising networks, namely, improve the Signal-to-Noise Ratio (SNR) of noisy networks. In this paper, we have explored the properties of network signal and noise and proposed a novel network denoising framework called Network Refinement (NR) that adjusts the edge weights by applying a nonlinear graph operator based on a diffusion process defined by random walk on the graph. Specifically, this unified framework consists of two closely linked approaches named NR-F and NR-B, which improve the SNR of noisy input networks from two different perspectives: NR-F aims at enhancing signal strength, while NR-B aims at weakening noise strength. Users can choose from which angle to improve the SNR of the network according to the characteristics of the network itself. We show that NR can significantly refine the quality of many networks by several applications on simulated networks and typical real-world biological and social networks., Comment: 20 pages, 7 figures, 1 table, 44 references, and 2 appendices. Submitted to IEEE Transactions on Network Science and Engineering