Quantifying the Effects of Topology and Weight for Link Prediction in Weighted Complex Networks

In weighted networks, both link weight and topological structure are significant characteristics for link prediction. In this study, a general framework combining null models is proposed to quantify the impact of the topology, weight correlation and statistics on link prediction in weighted networks. Three null models for topology and weight distribution of weighted networks are presented. All the links of the original network can be divided into strong and weak ties. We can use null models to verify the strong effect of weak or strong ties. For two important statistics, we construct two null models to measure their impacts on link prediction. In our experiments, the proposed method is applied to seven empirical networks, which demonstrates that this model is universal and the impact of the topology and weight distribution of these networks in link prediction can be quantified by it. We find that in the USAir, the Celegans, the Gemo, the Lesmis and the CatCortex, the strong ties are easier to predict, but there are a few networks whose weak edges can be predicted more easily, such as the Netscience and the CScientists. It is also found that the weak ties contribute more to link prediction in the USAir, the NetScience and the CScientists, that is, the strong effect of weak ties exists in these networks. The framework we proposed is versatile, which is not only used to link prediction but also applicable to other directions in complex networks.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

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

[3]  M. Newman.  Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Y. Lai,et al.  Characterization of weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  O. Sporns,et al.  Brain connectivity toolbox: a collection of complex network measurements and brain connectivity datasets. , 2009, NeuroImage.

[6]  Shi Zhou,et al.  The rich-club phenomenon in the Internet topology , 2003, IEEE Communications Letters.

[7]  Jonathan L. Herlocker,et al.  Evaluating collaborative filtering recommender systems , 2004, TOIS.

[8]  Linyuan Lü,et al.  Predicting missing links via local information , 2009, 0901.0553.

[9]  Tore Opsahl,et al.  Prominence and control: the weighted rich-club effect. , 2008, Physical review letters.

[10]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[11]  John Scott.  Social Network Analysis , 1988 .

[12]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Jon M. Kleinberg,et al.  The link-prediction problem for social networks , 2007, J. Assoc. Inf. Sci. Technol..

[14]  Ying Fan,et al.  Weighted networks of scientific communication: the measurement and topological role of weight , 2005 .

[15]  Gueorgi Kossinets.  Effects of missing data in social networks , 2006, Soc. Networks.

[16]  C. Leung,et al.  Weighted assortative and disassortative networks model , 2006, physics/0607134.

[17]  Lei Tian,et al.  Link prediction via significant influence , 2018 .

[18]  Buket Kaya,et al.  Age-series based link prediction in evolving disease networks , 2015, Comput. Biol. Medicine.

[19]  John E. Hopcroft,et al.  Using community information to improve the precision of link prediction methods , 2012, WWW.

[20]  Jian-Guo Liu,et al.  Detecting community structure in complex networks via node similarity , 2010 .

[21]  Yang Liu,et al.  Link Prediction , 2014, Encyclopedia of Social Network Analysis and Mining.

[22]  Mirella M. Moro,et al.  Social professional networks: A survey and taxonomy , 2017, Comput. Commun..

[23]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[24]  Julian Mintseris,et al.  A Protein Complex Network of Drosophila melanogaster , 2011, Cell.

[25]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[26]  Angelika Fruehauf.  Community Structure Of Complex Networks , 2016 .

[27]  Jing Zhao,et al.  Prediction of Links and Weights in Networks by Reliable Routes , 2015, Scientific Reports.

[28]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[29]  Bo Hu,et al.  General dynamics of topology and traffic on weighted technological networks. , 2005, Physical review letters.

[30]  Francesco Vaccarino,et al.  Topological Strata of Weighted Complex Networks , 2013, PloS one.

[31]  Lada A. Adamic,et al.  Friends and neighbors on the Web , 2003, Soc. Networks.

[32]  Tao Zhou,et al.  Empirical analysis of dependence between stations in Chinese railway network , 2009 .

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

[34]  Wenxu Wang,et al.  Modeling the coevolution of topology and traffic on weighted technological networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Donald E. Knuth,et al.  The Stanford GraphBase - a platform for combinatorial computing , 1993 .

[36]  Tao Zhou,et al.  Playing the role of weak clique property in link prediction: A friend recommendation model , 2016, Scientific Reports.

[37]  Peng Wang,et al.  Link prediction in social networks: the state-of-the-art , 2014, Science China Information Sciences.

[38]  Tansel Özyer,et al.  Link Prediction by Network Analysis , 2017, Prediction and Inference from Social Networks and Social Media.

[39]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[40]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Rushed Kanawati,et al.  Link Prediction in Complex Networks , 2020, Cognitive Analytics.

[42]  Hsinchun Chen,et al.  Link prediction approach to collaborative filtering , 2005, Proceedings of the 5th ACM/IEEE-CS Joint Conference on Digital Libraries (JCDL '05).

[43]  G. Bianconi.  Emergence of weight-topology correlations in complex scale-free networks , 2004, cond-mat/0412399.