Figure 1 illustrates how our notion of variance captures the variance of a graph distribution.
Fig. 1. The variance of distributions on a graph can be defined with respect to a distance function between the nodes of the graph. This measure allows us to compare how ‘spread out’ different distributions are on the network. In the example above, the distributions become more spread out over the network, going from distribution 1. → 4. with an increasing variance as a result; here, the variance is calculated with respect to the square root resistance distance as in equation (2.3).
## 2.3. ⇒ Distance Functions on Graphs.
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DEVRIENDT, Karel, MARTIN-GUTIERREZ, Samuel and LAMBIOTTE, Renaud, 2022. Variance and Covariance of Distributions on Graphs. SIAM Review. 5 May 2022. Vol. 64, no. 2, p. 343–359. DOI 10.1137/20M1361328, p. 4