Dynamics of social balance under temporal interaction

¹ National Institute of Informatics - 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
² JST, ERATO, Kawarabayashi Large Graph Project - 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
³ Department of Engineering Mathematics, Merchant Venturers Building, University of Bristol Woodland Road, Clifton, Bristol BS8 1UB, UK
⁴ CREST, JST - 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012, Japan
⁵ Department of Mathematical Informatics, The University of Tokyo - 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

^(a) naoki.masuda@bristol.ac.uk

Received: 19 March 2014
Accepted: 1 August 2014

Abstract

Real social contacts are often intermittent such that a link between a pair of nodes in a social network is only temporarily used. The effects of such temporal networks on social dynamics have been investigated for several phenomenological models such as epidemic spreading, linear diffusion processes, and nonlinear oscillations. Here, we numerically investigate nonlinear social balance dynamics in such a situation. Social balance is a classical psychological theory, which dictates that a triad is balanced if the three agents are mutual friends or if the two of them are the friends of each other and hostile to the other agent. We show that the social balance dynamics is slowed down on the temporal complete graph as compared to the corresponding static complete graph.