History effects on network growth

TL;DR

This paper introduces a fractional order differential equation model incorporating history effects into network growth, revealing that memory causes degree decay over time and influences hub formation.

Contribution

It presents a novel fractional differential equation model for network growth that accounts for historical effects, extending the classical Barabasi-Albert model.

Findings

Memory effects lead to degree decay over time.

Younger nodes have increased chances to become hubs.

Simulation and real network data confirm the impact of history on network dynamics.

Abstract

Growth dynamic of real networks because of emerging complexities is an open and interesting question. Indeed it is not realistic to ignore history impact on the current events. The mystery behind that complexity could be in the role of history in some how. To regard this point, the average effect of history has been included by a kernel function in differential equation of Barabasi Albert (BA) model . This approach leads to a fractional order BA differential equation as a generalization of BA model. As opposed to unlimited growth for degree of nodes, our results show that over time the memory impact will cause a decay for degrees. This gives a higher chance to younger members for turning to a hub. In fact in a real network, there are two competitive processes. On one hand, based on preferential attachment mechanism nodes with higher degree are more likely to absorb links. On the other hand, node history through aging process prevents new connections. Our findings from simulating a network grown by considering these effects also from studying a real network of collaboration between Hollywood movie actors conforms the results and significant effects of history and time on dynamic.