Parochial hexagons: the causes of contact number variation in territorial networks

The territorial networks that humans create are examples of cellular networks, a broad class of polygonal structures that share a consistent set of geometrical and topological properties. Hexagonal polygons predominate in cellular networks, but previous studies of territorial networks have failed to determine whether measuring polygon contact number provides useful information as to how the network evolved. Here we argue that this was due to a failure to integrate contact number measurements with an understanding of a network’s historical development. We analyse the contact number distribution of the English parish boundary network, uncovering a region of hexagonality that corresponds well to an area already known to be culturally and demographically distinctive in the early Middle Ages. Spatial variation in contact number in the English parish boundary network is shown not to be a simple function of topographical homogeneity and population density; instead, such relationships are mediated by spatial variation in tenurial and social systems. We conclude that the actual cause of hexagonality is more complex than often assumed in models of cellular network evolution, and that a holistic approach to the study of contact number can yield novel insights for landscape historians, historical geographers and spatial analysts.