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The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of segregation are implicitely tied to a single indicator, usually rely on an ambiguous definition of income classes, without any consensus on how to define neighbourhoods and to deal with the polycentric organization of large cities. In this paper, we address all these questions within a unique conceptual framework. We avoid the challenge of providing a direct definition of segregation and instead start from a definition of what segregation is not. This naturally leads to the measure of representation that is able to identify locations where categories are over- or underrepresented. From there, we provide a new measure of exposure that discriminates between situations where categories co-locate or repel one another. We then use this feature to provide an unambiguous, parameter-free method to find meaningful breaks in the income distribution, thus defining classes. Applied to the 2014 American Community Survey, we find 3 emerging classes—low, middle and higher income—out of the original 16 income categories. The higher-income households are proportionally more present in larger cities, while lower-income households are not, invalidating the idea of an increased social polarisation. Finally, using the density—and not the distance to a center which is meaningless in polycentric cities—we find that the richer class is overrepresented in high density zones, especially for larger cities. This suggests that density is a relevant factor for understanding the income structure of cities and might explain some of the differences observed between US and European cities. [ABSTRACT FROM AUTHOR]

This paper first reviews the descriptions and structural explanations for variations, in urban population densities in the United States over several decades. The research reviewed focuses on shifts in the technology and economics of travel as being the major influences on urban density distributions. These variables appear to be somewhat less adequate as explanations of the process in recent decades. After reviewing these findings and suggesting several research questions, we attempt to assess the evidence relating variations in population density to several other aspects of human behavior. A review of the research relating high population densities to various "social pathologies" indicates that little of the variance in rates of these pathologies can be attributed to density independently of other social structural variables. Some important consequences of population density have been reported, however, and possible research directions are outlined. [ABSTRACT FROM AUTHOR]