Local rewiring algorithms to increase clustering and grow a small world

Journal Article · 16 December 2018 · Journal of Complex Networks (Online)

DOI: https://doi.org/10.1093/comnet/cny032 · OSTI ID:1487187

Alstott, Jeff ^[1]; Klymko, Christine ^[2]; Pyzza, Pamela B. ^[3]; Radcliffe, Mary ^[4]; Moore, ed., Cristopher

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1. Massachusetts Institute of Technology/Singapore University of Technology and Design, MIT Media Lab, 77 Massachusetts Avenue, Cambridge, Ma
2. Lawrence Livermore National Laboratory, Center for Applied Scientific Computing, East Avenue, Livermore Ca
3. Department of Mathematics and Computer Science, Ohio Wesleyan University, 61 S Sandusky Drive, Delaware, Oh
4. Department of Mathematics, Carnegie Mellon University, Forbes Avenue, Pittsburgh, Pa

Abstract Many real-world networks have high clustering among vertices: vertices that share neighbours are often also directly connected to each other. A network’s clustering can be a useful indicator of its connectedness and community structure. Algorithms for generating networks with high clustering have been developed, but typically rely on adding or removing edges and nodes, sometimes from a completely empty network. Here, we introduce algorithms that create a highly clustered network by starting with an existing network and rearranging edges, without adding or removing them; these algorithms can preserve other network properties even as the clustering increases. They rely on local rewiring rules, in which a single edge changes one of its vertices in a way that is guaranteed to increase clustering. This greedy step can be applied iteratively to transform a random network into a form with much higher clustering. Additionally, the algorithms presented grow a network’s clustering faster than they increase its path length, meaning that network enters a regime of comparatively high clustering and low path length: a small world. These algorithms may be a basis for how real-world networks rearrange themselves organically to achieve or maintain high clustering and small-world structure.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1487187
• Journal Information: Journal of Complex Networks (Online), Journal Name: Journal of Complex Networks (Online) Journal Issue: 4 Vol. 7; ISSN 2051-1329
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United Kingdom
• Language: English