Title: Local rewiring algorithms to increase clustering and grow a small world

Abstract

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.

Authors:

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

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+ Show Author Affiliations

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

Publication Date:

Mon Dec 17 00:00:00 EST 2018

Research Org.:

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1487187

Alternate Identifier(s):

OSTI ID: 1811775

Report Number(s):

LLNL-JRNL-744604
Journal ID: ISSN 2051-1329

Grant/Contract Number:  

AC52-07NA27344

Resource Type:

Published Article

Journal Name:

Journal of Complex Networks (Online)

Additional Journal Information:

Journal Name: Journal of Complex Networks (Online) Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2051-1329

Publisher:

Oxford University Press

Country of Publication:

United Kingdom

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; mathematics and computing; clustering coefficient; small world; clustering; triangles