Can Spatiality Promote Diversity?

Real-world dynamics running on networks can be characterized in terms of their respective diversity, or heterogeneity of state values. Spatial networks can be understood as networks exhibiting limited small world characteristics. In the present work we argue that network spatiality can enhance the diversity of respectively unfolding dynamics. This also means that the small world property tends to reduce diversity. We illustrate this conjecture by simulating one type of Sznajd dynamics at the transient regime on Watts-Strogatz networks with varying rewiring levels. The obtained results show a marked reduction of state diversity as spatiality is replaced by the small world property.