Our group member Samuel Martin-Gutierrez and his collaborators have just published a new paper where they develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. This is a very versatile statistical tool that was missing in Network Science. The Network Variance can be used to measure social polarization, economic complexity, or interdisciplinarity in science. The Network Covariance provides a measure of correlation between two networks, and is applicable in fields such as neuroscience, to study the relationship between the functional and structural network of the brain.
Variance and Covariance of Distributions on Graphs
Karel Devriendt, Samuel Martin-Gutierrez, and Renaud Lambiotte
SIAM Review 2022 64:2, 343-359
Network Inequality Group 
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