Fractional Dynamics of Network Growth Constrained by aging Node Interactions

TL;DR

This paper introduces a fractional order Barabasi-Albert model incorporating aging effects, revealing how node aging influences network growth and hub formation, with applications demonstrated on Hollywood actor collaboration networks.

Contribution

It develops a fractional differential equation model for network growth with aging, extending the classic BA model and capturing decay in node connectivity over time.

Findings

Aging causes decay in node degrees over time.

Younger nodes have increased chances to become hubs.

Simulation results confirm the fractional model's predictions.

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 Barabasi-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.