Quantifying the Effect of Community Structures for Link Prediction by Constructing Null Models

The existing studies of link prediction mostly focused on using network topology properties to improve the accuracy of link prediction. More broadly, researches on the role of community structures for link prediction have recently received increasing attention. In this study, we propose a succinct algorithm that is built on community structures to improve the performance of link prediction, and it has been verified by both of synthetic benchmarks and real-world networks. More importantly, we introduce different null models to study the role of community structures on link prediction more carefully. Firstly, it is found that clearer community structures correspond to the higher performance of link prediction algorithms that are based on community information. Secondly, the role of links within a community and that between two communities are further distinguished. The edges within one community play a vital role for link prediction of the whole network, and conversely the edges between two communities have a minimal effect on that. At last, we reveal the relationship and dependence between this special meso-scale structure (community) and micro-scale structures of different orders (i.e., degree distribution, assortativity, and transitivity) for link prediction.

[1]  Sheng Hong,et al.  Failure cascade in interdependent network with traffic loads , 2015 .

[2]  Enrico Zio,et al.  A novel dynamics model of fault propagation and equilibrium analysis in complex dynamical communication network , 2014, Appl. Math. Comput..

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

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

[5]  Sheng Hong,et al.  Cascading failure analysis and restoration strategy in an interdependent network , 2016 .

[6]  Tao Zhou,et al.  Measuring multiple evolution mechanisms of complex networks , 2014, Scientific Reports.

[7]  Steve Gregory,et al.  Finding missing edges in networks based on their community structure , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  D. Lusseau,et al.  The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations , 2003, Behavioral Ecology and Sociobiology.

[9]  Dongyun Yi,et al.  The degree-related clustering coefficient and its application to link prediction , 2016 .

[10]  Kristina Lerman,et al.  Structure of Heterogeneous Networks , 2009, 2009 International Conference on Computational Science and Engineering.

[11]  Michael Small,et al.  Fitness networks for real world systems via modified preferential attachment , 2017 .

[12]  Giulio Cimini,et al.  Removing spurious interactions in complex networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[14]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[15]  Michael Small,et al.  The role of direct links for link prediction in evolving networks , 2017 .

[16]  Chiara Orsini,et al.  Quantifying randomness in real networks , 2015, Nature Communications.

[17]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[18]  Luis A Nunes Amaral.  A truer measure of our ignorance , 2008, Proceedings of the National Academy of Sciences.

[19]  Tao Zhou,et al.  Link prediction in weighted networks: The role of weak ties , 2010 .

[20]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Taewhan Kim,et al.  Community-Adaptive Link Prediction , 2017, DMCIT '17.

[22]  A. Barabasi,et al.  High-Quality Binary Protein Interaction Map of the Yeast Interactome Network , 2008, Science.

[23]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Hyeong Jun An,et al.  Estimating the size of the human interactome , 2008, Proceedings of the National Academy of Sciences.

[25]  James P. Bagrow.  Evaluating local community methods in networks , 2007, 0706.3880.

[26]  Judd Harrison Michael,et al.  Modeling the communication network in a sawmill , 1997 .

[27]  Jing Liu,et al.  A Multiobjective Evolutionary Algorithm Based on Similarity for Community Detection From Signed Social Networks , 2014, IEEE Transactions on Cybernetics.

[28]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

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

[30]  Boleslaw K. Szymanski,et al.  Towards Linear Time Overlapping Community Detection in Social Networks , 2012, PAKDD.

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

[32]  Priya Mahadevan,et al.  Orbis: rescaling degree correlations to generate annotated internet topologies , 2007, SIGCOMM '07.

[33]  Alneu de Andrade Lopes,et al.  Link Prediction in Complex Networks Based on Cluster Information , 2012, SBIA.

[34]  Shang Ke-k.  Construction and Application for Null Models of Complex Networks Based on Randomized Algorithms , 2014 .

[35]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[36]  Jing Xiao,et al.  Quantifying the Effects of Topology and Weight for Link Prediction in Weighted Complex Networks , 2018, Entropy.

[37]  Lidia A. Braunstein,et al.  Cascading failure and recovery of spatially interdependent networks , 2017 .

[38]  Neil Genzlinger.  A. and Q , 2006 .

[39]  P. Arabie,et al.  An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling , 1975 .

[40]  Enrique Herrera-Viedma,et al.  An incremental method to detect communities in dynamic evolving social networks , 2019, Knowl. Based Syst..

[41]  Weiming Shen,et al.  Link Prediction Based on Community Information and Its Parallelization , 2019, IEEE Access.

[42]  Masoud Asadpour,et al.  Link prediction in social networks using hierarchical community detection , 2015, 2015 7th Conference on Information and Knowledge Technology (IKT).

[43]  Weiming Shen,et al.  A vertex similarity index using community information to improve link prediction accuracy , 2017, 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

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

[45]  Michael Small,et al.  Evolving networks—Using past structure to predict the future , 2016 .

[46]  Santo Fortunato,et al.  Community detection in networks: A user guide , 2016, ArXiv.

[47]  Licheng Jiao,et al.  Prediction of missing links based on multi-resolution community division , 2015 .

[48]  P. Holme.  Network reachability of real-world contact sequences. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Kevin Chen-Chuan Chang,et al.  A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications , 2017, IEEE Transactions on Knowledge and Data Engineering.

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

[51]  Fang Liu,et al.  Prediction of missing links based on community relevance and ruler inference , 2016, Knowl. Based Syst..

[52]  Xiao-Ke Xu,et al.  Network embedding for link prediction: The pitfall and improvement. , 2019, Chaos.

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

[54]  Michael Small,et al.  Link direction for link prediction , 2017 .

[55]  Jing Xiao,et al.  Constructing null networks for community detection in complex networks , 2018, The European Physical Journal B.

[56]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[57]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[58]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[59]  Matthieu Latapy,et al.  Computing Communities in Large Networks Using Random Walks , 2004, J. Graph Algorithms Appl..

[60]  Timothy C. Havens,et al.  Quadratic Program-Based Modularity Maximization for Fuzzy Community Detection in Social Networks , 2015, IEEE Transactions on Fuzzy Systems.

[61]  Timothy Ravasi,et al.  From link-prediction in brain connectomes and protein interactomes to the local-community-paradigm in complex networks , 2013, Scientific Reports.

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

[63]  Qingguang Li,et al.  Link prediction based on hyperbolic mapping with community structure for complex networks , 2016 .

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

[65]  Yanchun Zhang,et al.  Node-coupling clustering approaches for link prediction , 2015, Knowl. Based Syst..

[66]  Jiye Liang,et al.  Exploiting user-to-user topic inclusion degree for link prediction in social-information networks , 2018, Expert Syst. Appl..

[67]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[68]  Michael Small,et al.  What exactly are the properties of scale-free and other networks? , 2013, ArXiv.