Related papers: Second to first order phase transition; coevolutio…
Both quantum phase transitions and thermodynamic phase transitions are probably induced by fluctuations, yet the specific mechanism through which fluctuations cause phase transitions remains unclear in existing theories. This paper…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
It is not uncommon for certain social networks to divide into two opposing camps in response to stress. This happens, for example, in networks of political parties during winner-takes-all elections, in networks of companies competing to…
Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) under the influence of the temperature modeling the social noise level are discussed for interacting actors occupying nodes of…
The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the…
We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social…
Does the enemy of my enemy become my friend? A growing literature on structural analysis of interstate relationships has tackled this old question from the network perspective. However, the mechanism of long-term change in the structure of…
We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…
We propose a thermodynamic multi-state spin model in order to describe equilibrial behavior of a society. Our model is inspired by the Axelrod model used in social network studies. In the framework of the statistical mechanics language, we…
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism…
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…
According to the so-called strong version of structural balance theory, actors in signed social networks avoid establishing triads with an odd number of negative links. Generalising, the weak version of balance theory allows for nodes to be…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. Considering a model representing dynamics on a one-dimensional…
Structural balance theory assumes triads in networks to gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for considering…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…