National-scale commuting geography: mapping and analyzing origin-destination matrices

Origin-Destination (OD) matrices are mathematical objects usually integrated inside transport models or treated as inputs for quantitative analysis. Trying to map an OD matrix is challenging due to the density and size of its data, and this often makes graphical representations unintelligible. Traditional approaches rely on partial matrices or aggregate indicators, limiting the spatial and relational insights that can be derived. This paper presents a novel analysis method that retains both the aggregate numerical quantities and the spatial relations between origins and destinations, providing a multidimensional representation of large-scale mobility patterns. The proposed approach is applied to two case studies: the 2011 commuting for work and study matrix of Italy, and the 2021 work commuting matrix of England and Wales. The Italian matrix has also been analyzed diachronically by mapping changes occurred between 1991 and 2011. Each case study demonstrates the method’s ability to reveal mobility trends and is used to describe and interpret the spatial structure of the territory and inform policies. The paper also discusses the method’s broader applicability and limitations, emphasizing its potential to enhance the interpretability of OD matrices across different contexts and using different data sources.