One of the most concerning aspects of the ongoing COVID-19 pandemic is that it disproportionately affects people from some specific ethnic and socio-economic minorities. In particular, since from the beginning of the pandemic it has been clear that people from Black and African American backgrounds seem to be hit especially hard by the virus, creating a substantial infection gap. The observed abnormal impact on these ethnic groups could probably be due to the co-occurrence of other known risk factors, including co-morbidity, poverty, level of education, access to healthcare, residential segregation and response to cures, although those factors do not seem able to explain fully and in depth the excess incidence of infections and deaths among African Americans. Here, we introduce the concept of diffusion segregation, that is the extent to which a given group of people is internally clustered or exposed to other groups, as a result of mobility and commuting habits. By analysing census and mobility data on major US cities, we found that the weekly excess COVID-19 incidence and mortality in African American communities at the beginning of the COVID-19 pandemic is significantly associated with their level of diffusion segregation. The results confirm that knowing where people commute to, rather than where they live, is potentially much more important to contain and curb the spreading of infectious diseases.

Socioeconomic segregation is considered one of the main factors behind the emergence of large-scale inequalities in urban areas, and its characterisation is an active area of research in urban studies. There are currently many available measures of spatial segregation, but almost all of them either depend in non-trivial ways on the scale and size of the system under study, or mostly neglect the importance of large-scale spatial correlations, or depend on parameters which make it hard to compare different systems on equal grounds. We propose here two non-parametric measures of spatial variance and local spatial diversity, based on the statistical properties of the trajectories of random walks on graphs. We show that these two quantities provide a consistent and intuitive estimation of segregation of synthetic spatial patterns, and we use them to analyse and compare the ethnic segregation of large metropolitan areas in the US and the UK. The results confirm that the spatial variance and local diversity as measured through simple diffusion on graphs provides meaningful insights about the spatial organisation of ethnicities across a city, and allows us to efficiently compare the ethnic segregation of urban areas across the world irrespective of their size, shape, or peculiar microscopic characteristics.

Socioeconomic segregation has an important role in the emergence of large-scale inequalities in urban areas. Most of the available measures of spatial segregation depend on the scale and size of the system under study, or neglect large-scale spatial correlations, or rely on ad-hoc parameters, making it hard to compare different systems on equal grounds. We propose here a family of non-parametric measures for spatial distributions, based on the statistics of the trajectories of random walks on graphs associated to a spatial system. These quantities provide a consistent estimation of segregation in synthetic spatial patterns, and we use them to analyse the ethnic segregation of metropolitan areas in the US and the UK. We show that the spatial diversity of ethnic distributions, as measured through diffusion on graphs, allow us to compare the ethnic segregation of urban areas having different size, shape, or peculiar microscopic characteristics, and exhibits a strong association with socio-economic deprivation.

Socioeconomic segregation is considered one of the main factors behind the emergence of largescale inequalities in urban areas, and its characterisation is an active area of research in urban studies. There are currently many available measures of spatial segregation, but almost all of them either depend in non-trivial ways on the scale and size of the system under study, or mostly neglect the importance of large-scale spatial correlations, or depend on parameters which make it hard to compare different systems on equal grounds. We propose here two non-parametric measures of spatial variance and local spatial diversity, based on the statistical properties of the trajectories of random walks on graphs. We show that these two quantities provide a consistent and intuitive estimation of segregation of synthetic spatial patterns, and we use them to analyse and compare the ethnic segregation of large metropolitan areas in the US and the UK. The results confirm that the spatial variance and local diversity as measured through simple diffusion on graphs provides meaningful insights about the spatial organisation of ethnicities across a city, and allows us to efficiently compare the ethnic segregation of urban areas across the world irrespective of their size, shape, or peculiar microscopic characteristics.