General

Several novel metrics have been proposed in recent literature in order to study the relative importance of nodes in complex networks. Among those, k-coreness has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system analysis and design. This paper proposes new distributed algorithms for the computation of the k-coreness of a network, a process also known as k-core decomposition. This technique 1) allows the decomposition, over a set of connected machines, of very large graphs, when size does not allow storing and processing them on a single host, and 2) enables the runtime computation of k-cores in “live” distributed systems. Lower bounds on the algorithms complexity are given, and an exhaustive experimental analysis on real-world data sets is provided.

[1]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[2]  Stephen B. Seidman,et al.  Network structure and minimum degree , 1983 .

[3]  Leslie G. Valiant,et al.  A bridging model for parallel computation , 1990, CACM.

[4]  Leslie G. Valiant,et al.  Direct Bulk-Synchronous Parallel Algorithms , 1992, J. Parallel Distributed Comput..

[5]  Leslie G. Valiant,et al.  Bulk synchronous parallel computing-a paradigm for transportable software , 1995, Proceedings of the Twenty-Eighth Annual Hawaii International Conference on System Sciences.

[6]  Afonso Ferreira,et al.  Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP , 1997, ICALP.

[7]  Gary D Bader,et al.  Analyzing yeast protein–protein interaction data obtained from different sources , 2002, Nature Biotechnology.

[8]  Vladimir Batagelj,et al.  An O(m) Algorithm for Cores Decomposition of Networks , 2003, ArXiv.

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

[10]  Alessandro Vespignani,et al.  Large scale networks fingerprinting and visualization using the k-core decomposition , 2005, NIPS.

[11]  Márk Jelasity,et al.  Gossip-based aggregation in large dynamic networks , 2005, TOCS.

[12]  Indranil Gupta,et al.  JetStream: Achieving Predictable Gossip Dissemination by Leveraging Social Network Principles , 2006, Fifth IEEE International Symposium on Network Computing and Applications (NCA'06).

[13]  Sergey N. Dorogovtsev,et al.  K-core Organization of Complex Networks , 2005, Physical review letters.

[14]  Jonathan W. Berry,et al.  Challenges in Parallel Graph Processing , 2007, Parallel Process. Lett..

[15]  Wei Cai,et al.  Using the k-core decomposition to analyze the static structure of large-scale software systems , 2010, The Journal of Supercomputing.

[16]  Márk Jelasity,et al.  PeerSim: A scalable P2P simulator , 2009, 2009 IEEE Ninth International Conference on Peer-to-Peer Computing.

[17]  Tom White,et al.  Hadoop: The Definitive Guide , 2009 .

[18]  Aart J. C. Bik,et al.  Pregel: a system for large-scale graph processing , 2010, SIGMOD Conference.

[19]  Jin-Soo Kim,et al.  HAMA: An Efficient Matrix Computation with the MapReduce Framework , 2010, 2010 IEEE Second International Conference on Cloud Computing Technology and Science.

[20]  Abraham Bernstein,et al.  Signal/Collect: Graph Algorithms for the (Semantic) Web , 2010, SEMWEB.

[21]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[22]  Ben Y. Zhao,et al.  Measurement-calibrated graph models for social network experiments , 2010, WWW '10.

[23]  Henri E. Bal,et al.  A High-Level Framework for Distributed Processing of Large-Scale Graphs , 2011, ICDCN.

[24]  Vladimir Batagelj,et al.  Fast algorithms for determining (generalized) core groups in social networks , 2011, Adv. Data Anal. Classif..

[25]  Nitesh V. Chawla,et al.  DisNet: A Framework for Distributed Graph Computation , 2011, 2011 International Conference on Advances in Social Networks Analysis and Mining.

[26]  James Cheng,et al.  Efficient core decomposition in massive networks , 2011, 2011 IEEE 27th International Conference on Data Engineering.

[27]  Sreenivas Gollapudi,et al.  Of hammers and nails: an empirical comparison of three paradigms for processing large graphs , 2012, WSDM '12.

[28]  Francesco De Pellegrini,et al.  Distributed k-Core Decomposition , 2013 .