Social Diffusion and Global Drift on Networks

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.

7 pages, 3 figures; to appear in Phys. Rev. E

References in corpus (8)

• Statistical physics of social dynamics
• Synchronization in complex networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Conservation laws for the voter model in complex networks
• Maximal-entropy random walks in complex networks with limited information
• Flow graphs: interweaving dynamics and structure
• Synchronization in weighed scale-free networks with degree-degree correlation
• Scaling of degree correlations and the influence on diffusion in scale-free networks

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