The degree variance: An index of graph heterogeneity
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TL;DR
For several types of graphs, the maximum value of the degree variance is given, and the mean and variance of the degrees variance under a simple stochastic null model are computed to produce normalized versions of thedegree variance, which can be used as heterogeneity indices of graphs.
Abstract
In the analysis of empirically found graphs, the variance of the degrees can be used as a measure for the heterogeneity of (the points in) the graph. For several types of graphs, the maximum value of the degree variance is given, and the mean and variance of the degree variance under a simple stochastic null model are computed. These are used to produce normalized versions of the degree variance, which can be used as heterogeneity indices of graphs.