Glassy states of aging social networks

TL;DR

This paper introduces a memory-based model into social network balance theory, revealing how aged relations create glassy states that slow down network evolution and influence the final balanced configurations.

Contribution

It incorporates a memory effect into the balance theory, demonstrating how aged social links lead to glassy states and affect the dynamics of social network evolution.

Findings

Memory prolongs the time to reach balanced states.

Aged links resist change, causing glassy states.

Final states remain similar, but evolution is slowed.

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