Measuring polycentricity via network flows, spatial interaction, and percolation

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Polycentricity, or the number of central urban places, is commonly measured by 10.1177_0042098019832517-fig1location-based metrics (e.g. employment density/total number of workers, above a threshold). While these metrics are good indicators of location ‘centricity’, results are sensitive to threshold choice. We consider the alternative idea that a centre’s status depends on its connectivity to other locations through trip inflows/outflows: this is inherently a network rather than placeidea. Three flow and network-based centricity metrics for measuring metropolitan area polycentricity using journey-to-work data are presented: (a) trip-based; (b) density-based; and (c) accessibility-based. Using these measures, polycentricity is computed and rank-centricity distributions are plotted to test Zipf-like or Christaller-like behaviours. Further, a percolation theory framework is proposed for the full origin–destination matrix, where trip flows are used as a thresholding parameter to count the number of sub-centres. Trip flows prove to be an effective measure to count and hierarchically organise metropolitan areas and sub-centres, tackling the arbitrariness of defining any threshold on employment statistics to count sub-centres. Applications on data from the Greater Sydney region show that the proposed framework helps to characterise polycentricity and sub-regional organisation more robustly, and provide unexpected insights into the connections between land use, labour market organisation, transport and urban structure.