Node similarity measuring in complex networks with relative entropy

Abstract Measuring the similarity of nodes in complex network has been significant research in the analysis of complex characteristic. Several existing methods have been proposed to address this problem, but most of them have their own limitations and shortcomings. So a novel method based on relative entropy is proposed to solve the problems above. The proposed entropy combines the fractal dimension of the whole network and the local dimension of each node on the basis of Tsallis entropy. When the fractal dimension equals to 1, the relative entropy would degenerate to classic form based on Shannon entropy. In addition, relevance matrix and similarity matrix are used to show the difference of structure and the similarity of each pair of nodes. The ranking results show the similarity degree of each node. In order to show the effectiveness of this method, four real-world complex networks are applied to measure the similarity of nodes. After comparing four existing methods, the results demonstrate the superiority of this method by employing susceptible-infected (SI) model and the ratio of mutual similar nodes.

[1]  Qi Zhang,et al.  Measure the structure similarity of nodes in complex networks based on relative entropy , 2018 .

[2]  Linyuan Lu,et al.  Link Prediction in Complex Networks: A Survey , 2010, ArXiv.

[3]  Wen Jiang,et al.  Evaluating Topological Vulnerability Based on Fuzzy Fractal Dimension , 2018, Int. J. Fuzzy Syst..

[4]  Haiyan Wang,et al.  Detecting early-warning signals in periodically forced systems with noise. , 2018, Chaos.

[5]  Ning Zhang,et al.  Effects of rewiring strategies on information spreading in complex dynamic networks , 2018, Commun. Nonlinear Sci. Numer. Simul..

[6]  Hao Liao,et al.  Information mining in weighted complex networks with nonlinear rating projection , 2017, Commun. Nonlinear Sci. Numer. Simul..

[7]  Mariano Sigman,et al.  A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks , 2011, Proceedings of the National Academy of Sciences.

[8]  Kecheng Liu,et al.  Common neighbour structure and similarity intensity in complex networks , 2017 .

[9]  Alessandro Vespignani,et al.  Dynamical Patterns of Epidemic Outbreaks in Complex Heterogeneous Networks , 1999 .

[10]  Wen Jiang,et al.  Identifying influential nodes based on fuzzy local dimension in complex networks , 2018, Chaos, Solitons & Fractals.

[11]  Yong Deng,et al.  Toward uncertainty of weighted networks: An entropy-based model , 2018, Physica A: Statistical Mechanics and its Applications.

[12]  M. Newman,et al.  Hierarchical structure and the prediction of missing links in networks , 2008, Nature.

[13]  Tao Wu,et al.  Predicting the evolution of complex networks via local information , 2016, ArXiv.

[14]  Linyuan Lu,et al.  SIMILARITY-BASED CLASSIFICATION IN PARTIALLY LABELED NETWORKS , 2010 .

[15]  Wen Jiang,et al.  A new information dimension of complex network based on Rényi entropy , 2019, Physica A: Statistical Mechanics and its Applications.

[16]  Yong Deng,et al.  A cluster-growing dimension of complex networks: From the view of node closeness centrality , 2019, Physica A: Statistical Mechanics and its Applications.

[17]  Bin Chen,et al.  Integrated evaluation approach for node importance of complex networks based on relative entropy , 2016 .

[18]  Pablo M. Gleiser,et al.  Community Structure in Jazz , 2003, Adv. Complex Syst..

[19]  Linyuan Lu,et al.  Link prediction based on local random walk , 2010, 1001.2467.

[20]  Shasha Wang,et al.  A modified efficiency centrality to identify influential nodes in weighted networks , 2019, Pramana.

[21]  Wen Jiang,et al.  A Novel Z-Network Model Based on Bayesian Network and Z-Number , 2020, IEEE Transactions on Fuzzy Systems.

[22]  Xinyang Deng,et al.  D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment , 2019, Int. J. Approx. Reason..

[23]  Tao Wen,et al.  Measuring the complexity of complex network by Tsallis entropy , 2019, Physica A: Statistical Mechanics and its Applications.

[24]  Wen Jiang,et al.  A correlation coefficient of belief functions , 2016, Int. J. Approx. Reason..

[25]  Yong Deng,et al.  A new measure of identifying influential nodes: Efficiency centrality , 2017, Commun. Nonlinear Sci. Numer. Simul..

[26]  Lixiang Li,et al.  General decay synchronization of complex multi-links time-varying dynamic network , 2019, Commun. Nonlinear Sci. Numer. Simul..

[27]  Degang Xu,et al.  Optimal control of an SIVRS epidemic spreading model with virus variation based on complex networks , 2017, Commun. Nonlinear Sci. Numer. Simul..

[28]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[29]  Luo-Qing Wang,et al.  Assessing the relevance of individual characteristics for the structure of similarity networks in new social strata in Shanghai , 2018, Physica A: Statistical Mechanics and its Applications.

[30]  Wen Jiang,et al.  An evidential dynamical model to predict the interference effect of categorization on decision making results , 2018, Knowl. Based Syst..

[31]  Vincent Gripon,et al.  SimiNet: A Novel Method for Quantifying Brain Network Similarity , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  E. Jonckheere,et al.  Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization , 2016, 1608.08192.

[33]  Yuankun Xue,et al.  Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications , 2017, Scientific Reports.

[34]  Dawei Zhao,et al.  Statistical physics of vaccination , 2016, ArXiv.

[35]  Yong Deng,et al.  Identification of influential nodes in network of networks , 2015, ArXiv.

[36]  Sankaran Mahadevan,et al.  Box-covering algorithm for fractal dimension of weighted networks , 2013, Scientific Reports.

[37]  Linyuan Lü,et al.  Similarity index based on local paths for link prediction of complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Xiaodong Li,et al.  Detecting overlapping community in complex network based on node similarity , 2015, Comput. Sci. Inf. Syst..

[39]  José S. Andrade,et al.  IMDB Network Revisited: Unveiling Fractal and Modular Properties from a Typical Small-World Network , 2013, PloS one.

[40]  Eric Rosenberg Non-monotonicity of the generalized dimensions of a complex network , 2017 .

[41]  Yong Deng,et al.  A novel visibility graph transformation of time series into weighted networks , 2018, Chaos, Solitons & Fractals.

[42]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[43]  Lada A. Adamic,et al.  The political blogosphere and the 2004 U.S. election: divided they blog , 2005, LinkKDD '05.

[44]  Eric Rosenberg Minimal partition coverings and generalized dimensions of a complex network , 2017 .

[45]  Tao Wen,et al.  An information dimension of weighted complex networks , 2018, Physica A: Statistical Mechanics and its Applications.

[46]  Yi-Cheng Zhang,et al.  Empirical analysis of web-based user-object bipartite networks , 2009, ArXiv.

[47]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[48]  Xingyuan Wang,et al.  Model for multi-messages spreading over complex networks considering the relationship between messages , 2017, Commun. Nonlinear Sci. Numer. Simul..

[49]  Hong Cheng,et al.  Link prediction via matrix completion , 2016, ArXiv.

[50]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[51]  Eric Rosenberg Maximal entropy coverings and the information dimension of a complex network , 2017 .

[52]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..