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    Structural sparsity of complex networks: bounded expansion in random models and real-world graphs

    Demaine, E.D. and Reidl, Felix and Rossmanith, P. and Villaamil Sánchez, F. and Sikdar, S. and Sullivan, B.D. (2019) Structural sparsity of complex networks: bounded expansion in random models and real-world graphs. Journal of Computer and System Sciences 105 , pp. 199-241. ISSN 0022-0000.

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    Abstract

    This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. Specifically, we give a new linear-time fpt algorithm for motif counting and linear time algorithms to compute localized variants of several centrality measures. To establish structural sparsity in real-world networks, we analyze several common network models regarding their structural sparsity. We show that, with high probability, (1) graphs sampled with a prescribed sparse degree sequence; (2) perturbed bounded-degree graphs; (3) stochastic block models with small probabilities; result in graphs of bounded expansion. In contrast, we show that the Kleinberg and the Barabási–Albert model have unbounded expansion. We support our findings with empirical measurements on a corpus of real-world networks.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): structural sparsity, bounded expansion, complex networks, random graphs, motif counting, centrality measures
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Felix Reidl
    Date Deposited: 03 Jun 2019 13:09
    Last Modified: 22 Aug 2019 10:25
    URI: http://eprints.bbk.ac.uk/id/eprint/27714

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