Asymptotic theory for the dynamic of networks with heterogenous social capital allocation

TL;DR

This paper develops an asymptotic theoretical framework for understanding the evolution of social networks with heterogeneous social capital allocation, validated by empirical data from various human interaction networks.

Contribution

It introduces a stochastic model with explicit asymptotic solutions for social network dynamics based on functional forms of activity and social capital.

Findings

Analytical predictions match empirical data accurately.

Scaling laws describe degree distribution evolution.

Model applicable to diverse social interaction networks.

Abstract

The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and challenge a rigorous dynamical system theory of network evolution. Here we study seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the node's activity and social capital allocation can be described by two general functional forms that can be used to define a simple stochastic model for social network dynamic. This model allows the explicit asymptotic solution of the Master Equation describing the system dynamic, and provides the scaling laws characterizing the time evolution of the social network degree distribution and individual node's ego network. The analytical predictions reproduce with accuracy the empirical observations validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other features of networks' formation and to generate data driven predictions for the asymptotic behavior of large-scale social networks.