Balance in signed networks

Alec Kirkley, George T. Cantwell, and M. E. J. Newman
Phys. Rev. E 99, 012320 – Published 22 January 2019

Abstract

We consider signed networks in which connections or edges can be either positive (friendship, trust, alliance) or negative (dislike, distrust, conflict). Early literature in graph theory theorized that such networks should display “structural balance,” meaning that certain configurations of positive and negative edges are favored and others are disfavored. Here we propose two measures of balance in signed networks based on the established notions of weak and strong balance, and we compare their performance on a range of tasks with each other and with previously proposed measures. In particular, we ask whether real-world signed networks are significantly balanced by these measures compared to an appropriate null model, finding that indeed they are, by all the measures studied. We also test our ability to predict unknown signs in otherwise known networks by maximizing balance. In a series of cross-validation tests we find that our measures are able to predict signs substantially better than chance.

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  • Received 21 September 2018

DOI:https://doi.org/10.1103/PhysRevE.99.012320

©2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
NetworksStatistical Physics & Thermodynamics

Authors & Affiliations

Alec Kirkley1, George T. Cantwell1, and M. E. J. Newman1,2

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 2Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA

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Issue

Vol. 99, Iss. 1 — January 2019

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