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Glassy States of Aging Social Networks

Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Krakow, Poland
Group of Researchers for Applications of Physics in Economy and Sociology (GRAPES), rue de la Belle Jardiniere 483, B-4031 Angleur, Belgium
School of Business, University of Leicester, University Road, Leicester LE1 7RH, UK
The Institute for Brain and Cognitive Science (IBCS), Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran
Center for Network Science, Central European University, H-1051 Budapest, Hungary
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Antonio M. Scarfone
Entropy 2017, 19(6), 246;
Received: 11 April 2017 / Revised: 12 May 2017 / Accepted: 14 May 2017 / Published: 30 May 2017
(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)
PDF [559 KB, uploaded 30 May 2017]


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 the 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 what is more, 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 configurations which live on stable states, such long-lived glassy states can survive in unstable states. View Full-Text
Keywords: glass state; social network; memory glass state; social network; memory

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Hassanibesheli, F.; Hedayatifar, L.; Safdari, H.; Ausloos, M.; Jafari, G.R. Glassy States of Aging Social Networks. Entropy 2017, 19, 246.

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