Giuseppe Facchetti, Giovanni Iacono, and Claudio Altafini, International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy

Edited by Giorgio Parisi, University of Rome, Italy, and approved October 26, 2011

PNAS
URL: http://www.pnas.org/content/108/52/20953.abstract

Abstract. Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly “apparent disorder,” rather than true “frustration.”