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Measuring segregation via analysis on graphs.(English)Zbl 1510.05179

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

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68T09 Computational aspects of data analysis and big data
91D30 Social networks; opinion dynamics
05C90 Applications of graph theory

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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