A system of cities is morphologically polycentric when its cities are similarly sized and evenly spaced across its territory. In this paper, we adapt established spatial interaction models and entropy-based measures of heterogeneity of weighted networks to the problem of measuring morphological polycentricity. We study the evolution of the morphological polycentricity of the system of English and Welsh towns from 1851 to 1881, a period characterised by rapid urbanisation and expansion of railways. Our approach enables us to account for morphological aspects of the system that are often neglected by existing measures of morphological polycentricity, such as the evolution of transport infrastructure and its impact on travel distances. We show that the trend towards a greater concentration of the population in fewer urban centres in England and Wales was accompanied by a more diverse network of connections and potential intercity interactions.
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