Exploring the low-energy landscape of large-scale signed social networks

G Facchetti, G Iacono, C Altafini - … Review E—Statistical, Nonlinear, and Soft …, 2012 - APS
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 2012APS
Analogously to a spin glass, a large-scale signed social network is characterized by the
presence of disorder, expressed in this context (and in the social network literature) by the
concept of structural balance. If, as we have recently shown, the signed social networks
currently available have a limited amount of true disorder (or frustration), it is also interesting
to investigate how this frustration is organized, by exploring the landscape of near-optimal
structural balance. What we obtain in this paper is that while one of the networks analyzed …
Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.
American Physical Society
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