Second to first order phase transition; coevolutionary versus structural balance

Abstract

In social networks, the balance theory has been studied by considering either the triple interactions between the links (structural balance) or the triple interaction of nodes and links (coevolutionary balance). In the structural balance theory, the links are not independent from each other, implying a global effect of this term and it leads to a discontinuous phase transition in the system's balanced states as a function of temperature. However, in the coevolutionary balance the links only connect two local nodes and a continuous phase transition emerges. In this paper, we consider a combination of both in order to understand which of these types of interactions will identify the stability of the network. We are interested to see how adjusting the robustness of each term versus the other might affect the system to reach a balanced state. We use statistical mechanics methods and the mean field theory and also the Monte-Carlo numerical simulations to investigate the behaviour of the order parameters and the total energy of the system. We find the phase diagram of the system which demonstrates the competition of these two terms at different ratios against each other and different temperatures. The system shows a tricritical point above which the phase transition switches from continuous to discrete. Also the superiority of the local perspective is observed at low temperatures and the global view will be the dominant term in determining the stability of the system at higher temperatures.

arXiv comment11 pages, 6 figures

References in corpus (21)

• Multirelational Organization of Large-scale Social Networks in an Online World
• The physics of higher-order interactions in complex systems
• Voter Model on Heterogeneous Graphs
• The statistical mechanics of networks
• Nonequilibrium phase transition in the coevolution of networks and opinions
• Dynamics of Social Balance on Networks
• Nonequilibrium phase transition in a model for social influence
• A General Formalism for Inhomogeneous Random Graphs
• Solution of the 2-star model of a network
• Optimal Containment of Epidemics in Temporal and Adaptive Networks
• Solution for the properties of a clustered network
• Fragmentation versus Stability in Bimodal Coalitions
• Statistical Physics of Balance Theory
• Balance and Frustration in Signed Networks
• Measuring Partial Balance in Signed Networks
• Mean-field solution of structural balance dynamics in nonzero temperature
• Homophily based on few attributes can impede structural balance
• Altered structural balance of resting-state networks in autism
• Absorbing transition in a coevolution model with node and link states in an adaptive network: Network fragmentation transition at criticality
• Heider and coevolutionary balance: From discrete to continuous phase transition
• Hybrid balance theory: Heider balance under higher order interactions