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.
Keywords
- Diffusion process
- Boards of Directors
- Women on boards
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Acknowledgments
This research has received financial support by the Spanish Government (Project I+D+i PID2020-114183RB-I00, funded by AEI/FEDER, UE). We are also thankful to Rosa Benito, Javier Borondo, Ernesto Estrada, Juan Carlos Losada and Miguel Rebollo, as well as the participants in the Mediterranean Summer School on Complex Networks and the International Conference on Nonlinear Mathematics and Physics for their comments and suggestions.
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Gimeno, R., de Cabo, R.M., Grau, P., Gabaldon, P. (2022). Asymmetric Diffusion in a Complex Network: The Presence of Women on Boards. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol 1072. Springer, Cham. https://doi.org/10.1007/978-3-030-93409-5_62
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DOI: https://doi.org/10.1007/978-3-030-93409-5_62
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