title: Fractional Dynamics of Network Growth Constrained by Aging Node Interactions.
abstract: In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node's age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model.
authors.affiliation: Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.
authors.forename: Hadiseh
authors.initials: H
authors.lastname: Safdari
authors.affiliation: Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.
authors.forename: Milad
authors.initials: M
authors.lastname: Zare Kamali
authors.affiliation: Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.
authors.forename: Amirhossein
authors.initials: A
authors.lastname: Shirazi
authors.affiliation: Department of Mathematics, Tarbiat Modares University, Tehran, Iran.
authors.forename: Moein
authors.initials: M
authors.lastname: Khalighi
authors.affiliation: Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.|The Institute for Brain and Cognitive Science (IBCS), Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.|Center for Network Science, Central European University, Nador 9, 1051 Budapest, Hungary.
authors.forename: Gholamreza
authors.initials: G
authors.lastname: Jafari
authors.affiliation: GRAPES, rue de la Belle Jardiniere 483, B-4031, Angleur, Belgium.|School of Management, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom.|eHumanities group, Royal Netherlands Academy of Arts and Sciences, Joan Muyskenweg 25, 1096 CJ, Amsterdam, The Netherlands.
authors.forename: Marcel
authors.initials: M
authors.lastname: Ausloos
mesh_terms: D000375:Aging / Q000502:physiology*; D000465:Algorithms; D001363:Awards and Prizes; D003198:Computer Simulation; D003299:Cooperative Behavior; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011336:Probability; D012944:Social Support