Glassy states of aging social networks

Abstract

Individuals often develop reluctance to change their social relations, called "secondary homebody", even though their interactions with their environment evolve with time. Some memory effect is loosely present deforcing changes. In other words, in presence of memory, relations do not change easily. In order to investigate some history or memory effect on social networks, we introduce a temporal kernel function into the Heider conventional balance theory, allowing for the "quality" of past relations to contribute to the evolution of the system. This memory effect is shown to lead to the emergence of aged networks, thereby perfectly describing and the more so measuring the aging process of links ("social relations"). It is shown that such a memory does not change the dynamical attractors of the system, but does prolong the time necessary to reach the "balanced states". The general trend goes toward obtaining either global ("paradise" or "bipolar") or local ("jammed") balanced states, but is profoundly affected by aged relations. The resistance of elder links against changes decelerates the evolution of the system and traps it into so named glassy states. In contrast to balance

12 pages, 3 figures, 64 references

References in corpus (15)

• Multirelational Organization of Large-scale Social Networks in an Online World
• The Slashdot Zoo: Mining a Social Network with Negative Edges
• Social Balance on Networks: The Dynamics of Friendship and Enmity
• Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model
• Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game
• Self-organization towards optimally interdependent networks by means of coevolution
• Dynamical and bursty interactions in social networks
• Social network dynamics of face-to-face interactions
• How memory generates heterogeneous dynamics in temporal networks
• Aging Scaled Brownian Motion
• Epidemic spreading on evolving signed networks
• Fractional Dynamics of Network Growth Constrained by aging Node Interactions
• Fractional calculus ties the microscopic and macroscopic scales of complex network dynamics
• Gain and loss of esteem, direct reciprocity and Heider balance
• Statistical-mechanics approach to a reinforcement learning model with memory

Cited by in corpus (2)

• Mean-field solution of structural balance dynamics in nonzero temperature
• Dynamics of Social Balance on Networks: The Emergence of Multipolar Societies