Quartic Balance Theory: Global Minimum With Imbalanced Triangles

Abstract

Balance theory proposed by Heider for the first time modeled triplet interaction in a signed network, stating that relationships between two people, friendship or enmity, is dependent on a third person. The Hamiltonian of this model has an implicit assumption that all triads are independent, meaning that state of each triad, being balanced or imbalanced, is ineffective to others. This independence forces the network to have completely balanced final states. However, there exists evidence indicating that real networks are partially balanced raising the question of what is the mechanism preventing the system to be perfectly balanced. Our suggestion is to consider a quartic interaction which dissolves the triad's independence. We use mean field method to study thermal behavior of such systems where the temperature is a parameter that allows the stochastic behavior of agents. We show that under a certain temperature, the symmetry between balanced and imbalanced triads will spontaneously break and we have a discrete phase transition. As consequence stability arises where either similar balanced or imbalanced triads dominate, hence the system obtains two new imbalanced stable states. In this model, the critical temperature depends on the second power of the number of nodes, which was a linear dependence in thermal balance theory. Our simulations are in good agreement with the results obtained by the mean field method.

References in corpus (23)

• Multirelational Organization of Large-scale Social Networks in an Online World
• The statistical mechanics of networks
• The Statistical Physics of Real-World Networks
• Dynamics of Social Balance on Networks
• Analysis of a continuous-time model of structural balance
• Social Balance on Networks: The Dynamics of Friendship and Enmity
• The energy landscape of social balance
• Solution of the 2-star model of a network
• The Heider balance - a continuous approach
• Optimal Containment of Epidemics in Temporal and Adaptive Networks
• Balance in signed networks
• Solution for the properties of a clustered network
• Fragmentation versus Stability in Bimodal Coalitions
• Statistical Physics of Balance Theory
• Epidemic spreading on evolving signed networks
• Mean-field solution of structural balance dynamics in nonzero temperature
• Competing Effects of Social Balance and Influence
• Glassy states of aging social networks
• Dynamic Peer-to-Peer Competition
• Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks
• Cooperative peer-to-peer multiagent based systems
• Effects of Competition and Cooperation Interaction between Agents on Networks in Presence of a "Market Capacity"
• Dynamical phase diagrams of a love capacity constrained prey-predator model

Cited by in corpus (13)

• Altered structural balance of resting-state networks in autism
• Heider Balance under Disordered Triadic Interactions
• Competitive Balance Theory: Modeling conflict of interest in a heterogeneous network
• Mean-Field Solution for Critical Behavior of Signed Networks in Competitive Balance Theory
• Heider and coevolutionary balance: From discrete to continuous phase transition
• The structure of gene-gene networks beyond pairwise interactions
• Hybrid balance theory: Heider balance under higher order interactions
• Modified Heider Balance on Sparse Random Networks
• Financial Crisis in the Framework of Non-zero Temperature Balance Theory
• Patterns of link reciprocity in directed, signed networks
• Response of the competitive balance model to the external field
• Individual versus Social Benefit on the Heterogeneous Networks
• Heider balance on Archimedean lattices and cliques