  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.
