  Urban systems are primarily relational. The uneven intensities and
distribution of flows between systems of cities results in hierarchically
organised complex networks of urban exchange. Distinct urban spatial structures
reflect the diversity of functional and social patterns which vary or remain
constant across multiple scales. In this work, we examine the impact of
commuting on the potential accessibility to spatial and social diversity, and
the scalar relations that may exist. We first define relational scales by
conducting a process of percolation on the commuting network, as a hierarchical
clustering algorithm. This gives rise to a nested structure of urban clusters
based on flow connectivity. For each cluster at each scale, we compute measures
of commuting structural and social diversity by examining the spatial
distribution of origin-destination pairs, and the distribution of workers'
skills and occupations. To do this, we make use of global entropy measures
allowing us to quantitatively analyse the reachable diversity across scales.
Applying this methodology to Chile, we observe that the hierarchical
accessibility to the wider system of cities and the patterns of spatial
interaction, significantly influence the degree of exposure to diversity within
urban systems. This framework examines connectivity-based diversity at multiple
scales, and allows for the classification of cities and systems of cities
according to the spatial and social dimensions of commuting dispersion. Such
insights could contribute to the planning of infrastructural projects
connecting the urban system at different scales, while also guiding a strategic
relocation and redistribution of economic activities at regional levels.
