Giscard, Pierre-Louis, Rochet, Paul and Wilson, Richard Charles orcid.org/0000-0001-7265-3033 (2017) Evaluating balance on social networks from their simple cycles. Journal of Complex Networks. pp. 1-26. ISSN 2051-1329
Abstract
Signed networks have long been used to represent social relations of amity (+) and enmity (-) between individuals. Group of individuals who are cyclically connected are said to be balanced if the number of negative edges in the cycle is even and unbalanced otherwise. In its earliest and most natural formulation, the balance of a social network was thus defined from its simple cycles, cycles which do not visit any vertex more than once. Because of the inherent difficulty associated with finding such cycles on very large networks, social balance has since then been studied via other means. In this article we present the balance as measured from the simple cycles and primitive orbits of social networks. We specifically provide two measures of balance: the proportion R` of negative simple cycles of length ` for each ` 6 20 which generalises the triangle index, and a ratio K` which extends the relative signed clustering coefficient introduced by Kunegis. To do so, we use a Monte Carlo implementation of a novel exact formula for counting the simple cycles on any weighted directed graph. Our method is free from the double-counting problem affecting previous cycle-based approaches, does not require edge-reciprocity of the underlying network, provides a gray-scale measure of balance for each cycle length separately and is sufficiently tractable that it can be implemented on a standard desktop computer. We observe that social networks exhibit strong inter-edge correlations favouring balanced situations and we determine the corresponding correlation length x . For longer simple cycles, R` undergoes a sharp transition to values expected from an uncorrelated model. This transition is absent from synthetic random networks, strongly suggesting that it carries a sociological meaning warranting further research.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The authors 2017. Published by Oxford University Press. All rights reserved.This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details. |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Computer Science (York) |
Depositing User: | Pure (York) |
Date Deposited: | 21 Jun 2017 14:00 |
Last Modified: | 16 Oct 2024 13:51 |
Status: | Published |
Refereed: | Yes |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:118001 |