Segregation, income polarization, and spatial autocorrelation belong to separate literatures, though each asks how an attribute is arranged across a map. Their measures fit in one table, set by two choices: whether the attribute keeps the size of each unit’s departure from the regional composition, and whether the graph of neighboring units is read by its sum or by an eigenvalue. One combination is unused. The project fills it with a spatial concordance index, K, which joins neighboring units that depart from the regional composition in the same direction and reports the share of the achievable concordance a map attains, net of chance.
K splits exactly into the two sides of an income threshold, so sweeping the threshold locates where in a region’s income distribution its geography is most organized, and how that organization divides between the region’s more and less affluent neighborhoods. California’s metropolitan areas are the first application. The empirical sequel, Separated, Polarized, and Factioned?, covers every U.S. metropolitan region from 2010 to 2025.