Structural sparsity of complex networks: Bounded expansion in random models and real-world graphs
Author(s)Demaine, Erik D
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This research establishes that many real-world networks exhibit bounded expansion2, 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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal of Computer and System Sciences
Demaine, Erik D. et al. “Structural sparsity of complex networks: Bounded expansion in random models and real-world graphs.” Journal of Computer and System Sciences, 105 (November 2019): 199-241 © 2019 The Author(s)