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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 6: Dynamics of Social and Adaptive Networks I

SOE 6.2: Vortrag

Donnerstag, 30. September 2021, 12:15–12:45, H3

Balanced Triad Formation explained by Dyadic Interactions — •Tuan Pham^1,2, Jan Korbel^1,2, Rudolf Hanel^1,2, and Stefan Thurner^1,2,3 — ¹Medical University of Vienna — ²Complexity Science Hub Vienna — ³Santa Fe Institute

The evolution of social (signed) triads towards so-called balanced states with either one or three positive links often results in the formation of clusters of positively-linked agents. We argue that –surprisingly– such cluster formation can emerge from dyadic interactions if homophily between agents is present. We show this in a Hamiltonian model, where every agent is linked to K others and holds binary opinions on G issues, in an opinion vector s_i. If two agents i and j are connected by a link J_ij then J_ij = sign(s_i · s_j). Without knowledge of the triads in their neighbourhoods, agents modify their opinions so as to minimize a social tension, H⁽ⁱ⁾, defined via the weighted sum of opinion overlaps with friends and opinion discordance with enemies: H⁽ⁱ⁾ = − α/G · ∑ _{j: Jij > 0}s_i s_j + 1 − α/G · ∑ _{j: Jij < 0} s_is_j , where α is the relative strength of positive interactions to that of negative ones. The model exhibits a transition from unbalanced- to balanced society at a critical temperature which depends on (G, K , α). As α exceeds 1/2, another transition between steady states with different fractions of balanced triads occurs. We show that the model explains actual data of triad statistics in social networks. The model produces z-scores for triads that is compatible with empirical values in real social networks, such as the Pardus computer game and the United Nations General Assembly.