Social Diffusion and Global Drift on Networks

TL;DR

This paper models social diffusion on networks, revealing how local interactions cause the global state to drift upward or remain neutral, and proposes an adaptive method to maximize this drift for social influence applications.

Contribution

It introduces a mathematical model of social diffusion that accounts for non-conservation of the global state and proposes an adaptive link weight adjustment method to enhance upward global drift.

Findings

Global state drifts upward or remains neutral depending on strength-state correlation.

Strength assortativity slows down the homogenization process.

Adaptive link weight adjustment can maximize upward global drift.

Abstract

We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is not state conservational and thus the global state of the network (i.e., sum of node states) will drift. The asymptotic average node state will be the average of initial node states weighted by their strengths. Here we show that, while the global state is not conserved in this process, the inner product of strength and state vectors is conserved instead, and perfect positive correlation between node states and local averages of their self/neighbor strength ratios always results in upward (or at least neutral) global drift. We also show that the strength assortativity negatively affects the speed of homogenization. Based on these findings, we propose an adaptive link weight adjustment method to achieve the highest upward global drift by increasing the strength-state correlation. The effectiveness of the method was confirmed through numerical simulations and implications for real-world social applications are discussed.