Fractional Dynamics of Network Growth Constrained by Aging Node Interactions.

Area of Science:

• Complex Systems Science
• Network Science
• Sociophysics

Background:

• Social complex systems exhibit non-linear interactions where historical events shape network dynamics.
• The influence of "commonly accepted beliefs" or agent age on network growth remains understudied.
• Existing models like preferential attachment do not fully capture the impact of time on network evolution.

Purpose of the Study:

• To investigate how past circumstances, specifically agent age, influence the growth process of social networks.
• To generalize the Barabási-Albert (BA) model by incorporating a time-dependent kernel function.
• To analyze the competitive dynamics between preferential attachment and network aging.

Main Methods:

• Modification of the preferential attachment mechanism by introducing a time-dependent kernel function.
• Development of a fractional order Barabási-Albert (BA) differential equation to model network evolution.
• Simulations of network growth incorporating the aging constraint.
• Analysis of a real-world Hollywood actor collaboration network.

Main Results:

• An observed aging process in network dynamics leads to a decay in node degree values over time.
• Agent age acts as an opposing force to preferential attachment, reducing connection chances for older nodes.
• This competitive scenario increases the likelihood of younger nodes becoming network hubs.
• Empirical data from Hollywood actor collaborations show a decay in collaboration rates, with sex differences noted.

Conclusions:

• The generalized BA model with aging provides a more comprehensive understanding of social network evolution.
• Network aging is a significant factor, creating a balance between established and new network members.
• The findings suggest broad applicability of the generalized model across various complex systems, including social and collaboration networks.