3 - Emergence of Stable and Glassy States in Dynamics of Social Networks

Abstract

The dynamics of social networks based on Heider's balance theory moves toward lower tension states. The conditions derived from this theory enforce the agents to reevaluate and modify their interactions to achieve equilibrium. The final destination of these systems could reside on local (jammed states) or global (balanced states) minimum tension states. These states are stable ones that changing each relation leads to an increase of tension in the society. There is a margin before jammed states where the number of possible paths ending to them drastically decreases. Inverse participation ratio method could be used as an indicator to predict jammed states in advance. This method uses adjacency matrix at each time step to calculate participation of individuals. Moreover, adding the effect of gain and loss of esteem on the evolution of relations breaks the symmetry of relations and increases the emergence of jammed states. The other important parameter in social interactions is history or memory of relations. Over time, inclination to change aged relations decrease despite they can evolve based on Heider's balance conditions. This process decelerates the evolution of the system and leads to the formation of aged societies. So societies live for long times in states called glassy states with no inclination to reduce tension.