Measuring Segregation via Analysis on Graphs

In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus a classical statistic from the geography and urban sociology literature known as Moran’s , which in our language is score associated real-valued function graph, computed with respect spatial weight matrix such adjacency geographic units that tile city. Our results characterizing extremal behavior illustrate important role underlying graph structure, especially degree distribution, interpreting score. addition standard matrices encoding unit adjacency, consider Laplacian doubly-stochastic approximation . These alternatives allow us connect ideas Fourier random walks. offer illustrations theoretical mix stylized synthetic examples real geographic/demographic data.