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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 6: Dynamics of Social and Adaptive Networks I

SOE 6.2: Talk

Thursday, September 30, 2021, 12:15–12:45, H3

Balanced Triad Formation explained by Dyadic Interactions — •Tuan Pham1,2, Jan Korbel1,2, Rudolf Hanel1,2, and Stefan Thurner1,2,31Medical 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 si. If two agents i and j are connected by a link Jij then Jij = sign(si · sj). 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 > 0si sj + 1 − α/G · ∑ j: Jij < 0 sisj , 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.

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