Fast and simple decycling and dismantling of networks

Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple and considerably sub-optimal, on the one hand, and involved and accurate message-passing ones that evaluate single-node marginal probabilities, on the other hand. In this paper we propose a simple and extremely fast algorithm, CoreHD, which recursively removes nodes of the highest degree from the 2-core of the network. CoreHD performs much better than all existing simple algorithms. When applied on real-world networks, it achieves equally good solutions as those obtained by the state-of-art iterative message-passing algorithms at greatly reduced computational cost, suggesting that CoreHD should be the algorithm of choice for many practical purposes.

[1]  D. Bu,et al.  Topological structure analysis of the protein-protein interaction network in budding yeast. , 2003, Nucleic acids research.

[2]  Guilhem Semerjian,et al.  Network dismantling , 2016, Proceedings of the National Academy of Sciences.

[3]  Ian T. Foster,et al.  Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design , 2002, ArXiv.

[4]  Jure Leskovec,et al.  Friendship and mobility: user movement in location-based social networks , 2011, KDD.

[5]  Hai-Jun Zhou,et al.  Identifying optimal targets of network attack by belief propagation , 2016, Physical review. E.

[6]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[7]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[8]  Bruce M. Maggs,et al.  Globally Distributed Content Delivery , 2002, IEEE Internet Comput..

[9]  Christos Faloutsos,et al.  Graphs over time: densification laws, shrinking diameters and possible explanations , 2005, KDD '05.

[10]  Elchanan Mossel,et al.  Spectral redemption in clustering sparse networks , 2013, Proceedings of the National Academy of Sciences.

[11]  Pan Zhang.  Nonbacktracking operator for the Ising model and its applications in systems with multiple states. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[13]  Marko Bajec,et al.  Robust network community detection using balanced propagation , 2011, ArXiv.

[14]  Jeffrey Shaman,et al.  Collective influence maximization in threshold models of information cascading with first-order transitions , 2016, ArXiv.

[15]  Shao-Meng Qin,et al.  Spin-glass phase transitions and minimum energy of the random feedback vertex set problem. , 2016, Physical review. E.

[16]  Riccardo Zecchina,et al.  Optimizing spread dynamics on graphs by message passing , 2012, 1203.1426.

[17]  Sanming Zhou,et al.  Decycling numbers of random regular graphs , 2002, Random Struct. Algorithms.

[18]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[19]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[20]  Kyomin Jung,et al.  IRIE: Scalable and Robust Influence Maximization in Social Networks , 2011, 2012 IEEE 12th International Conference on Data Mining.

[21]  G. Semerjian,et al.  Minimal Contagious Sets in Random Regular Graphs , 2014, 1407.7361.

[22]  Hernán A. Makse,et al.  Influence maximization in complex networks through optimal percolation , 2015, Nature.

[23]  Antonio Politi,et al.  Immunization and targeted destruction of networks using explosive percolation , 2016, Physical review letters.

[24]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[25]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[26]  Svante Janson,et al.  Dismantling Sparse Random Graphs , 2007, Combinatorics, Probability and Computing.

[27]  Matthew Richardson,et al.  Mining knowledge-sharing sites for viral marketing , 2002, KDD.

[28]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[29]  Hai-Jun Zhou,et al.  Spin glass approach to the feedback vertex set problem , 2013, 1307.6948.

[30]  Christian Borgs,et al.  Maximizing Social Influence in Nearly Optimal Time , 2012, SODA.