Asymmetric Diffusion in a Complex Network: The Presence of Women on Boards

Abstract

Diffusion processes are well known linear dynamical systems. However, a different kind of dynamical solutions emerge when the speed of diffusion is dependent on the sign of the gradient variable that is diffused through the graph. In this case, we move into a nonlinear dynamical system where solutions would depend on the differential speed of diffusion, the topological structure of the graph and the initial values of the gradient variable. We show an example in a real complex network: we construct a network of US Boards of Directors, where nodes are boards, and links are interlocking directorates. We show that the proportion of women on each board follows a diffusion process, where changes depend of the gradient of this proportion to adjacent boards. Furthermore, we show that the diffusion is asymmetric, with diffusion slower(faster) when the board has a lower(higher) proportion of women than neighbor boards.