S-BITE: A Structure-Based Internet Topology gEnerator

The modeling and analysis of large-scale complex systems, such as the Internet, has recently become a hot research topic. We propose a Structure-Based Internet Topology gEnerator (S-BITE) aimed at accurately reproducing the Internet at the Autonomous System (AS) level. The proposed generator exploits a technique that partitions the network topology into two distinct blocks: the Core, which captures the underlying community structure of the Internet, and the Periphery, representing the "tendrils" of the topology. The benefits of this innovative technique are twofold. First, it deals with the high heterogeneity of the Internet by highlighting a small yet well-structured core. This leads to a huge reduction in complexity and shows that the core of the large-scale Internet is not that large, and can further be broken down into a two-layer graph. Second, thanks to the simplifications introduced by the topology layering, it leads us to the definition of a new topology generator, first at the core level and then for the whole Internet.To the best of our knowledge, S-BITE is the first generator that successfully targets the problem of both matching classical graph metrics, such as the degree distribution, and representing the Internets structure, in the form of maximal cliques. A comparison shows how S-BITE outperforms the reference generators in the literature when looking at both statistical and structural properties of the Internet.

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

[2]  Michalis Faloutsos,et al.  Jellyfish: A conceptual model for the as Internet topology , 2006, Journal of Communications and Networks.

[3]  Alessandro Vespignani,et al.  K-core Decomposition: a Tool for the Visualization of Large Scale Networks , 2005, ArXiv.

[4]  Lun Zhang,et al.  The Watts–Strogatz network model developed by including degree distribution: theory and computer simulation , 2007 .

[5]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Chiara Orsini,et al.  C Consiglio Nazionale delle Ricerche The Impact of IXPs on the AS-level Topology Structure of the Internet , 2010 .

[7]  Yuval Shavitt,et al.  A model of Internet topology using k-shell decomposition , 2007, Proceedings of the National Academy of Sciences.

[8]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[10]  M. Markus,et al.  Oscillations and turbulence induced by an activating agent in an active medium. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Amogh Dhamdhere,et al.  The Internet is flat: modeling the transition from a transit hierarchy to a peering mesh , 2010, CoNEXT.

[12]  A. Wool,et al.  A clustering approach for exploring the Internet structure , 2004, 2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel.

[13]  Karl Pearson F.R.S..  X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling , 2009 .

[14]  Ellen W. Zegura,et al.  A quantitative comparison of graph-based models for Internet topology , 1997, TNET.

[15]  Anukool Lakhina,et al.  BRITE: Universal Topology Generation from a User''s Perspective , 2001 .

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

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

[18]  Enrico Gregori,et al.  Parallel $(k)$-Clique Community Detection on Large-Scale Networks , 2013, IEEE Transactions on Parallel and Distributed Systems.

[19]  Mao-Bin Hu,et al.  Detect overlapping and hierarchical community structure in networks , 2008, ArXiv.

[20]  Xiaogang Jin,et al.  Linking via social similarity: The emergence of community structure in scale-free network , 2009, 2009 1st IEEE Symposium on Web Society.

[21]  Walter Willinger,et al.  The origin of power laws in Internet topologies revisited , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[22]  J. Moon,et al.  On cliques in graphs , 1965 .

[23]  Sugih Jamin,et al.  Inet-3.0: Internet Topology Generator , 2002 .

[24]  Lixia Zhang,et al.  The (In)Completeness of the Observed Internet AS-level Structure , 2010, IEEE/ACM Transactions on Networking.

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

[26]  Miguel Rio,et al.  Network topologies: inference, modeling, and generation , 2008, IEEE Communications Surveys & Tutorials.

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

[28]  B. Bollobás.  The evolution of random graphs , 1984 .

[29]  Fergal Reid,et al.  Detecting highly overlapping community structure by greedy clique expansion , 2010, KDD 2010.

[30]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[31]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[32]  Walter Willinger,et al.  10 Lessons from 10 Years of Measuring and Modeling the Internet's Autonomous Systems , 2011, IEEE Journal on Selected Areas in Communications.

[33]  Samir Khuller,et al.  On Finding Dense Subgraphs , 2009, ICALP.

[34]  Dmitri Loguinov,et al.  Understanding and modeling the internet topology: economics and evolution perspective , 2010, TNET.

[35]  Walter Willinger,et al.  Scaling phenomena in the Internet: Critically examining criticality , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Chiara Orsini,et al.  k-dense communities in the internet AS-level topology , 2011, 2011 Third International Conference on Communication Systems and Networks (COMSNETS 2011).

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