Samuel Martin-Gutierrez presents a work pursued together with Karel Devriendt and Renaud Lambiotte at the 10th International Conference on Complex Networks and their Applications, which took place as a hybrid event in Madrid from Nov 30th to Dez 2, 2021 in Madrid.
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a network, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of weighted networks and retains many of its intuitive and desired properties.
We have applied the variance and ovariance measures to the analysis of two empirical networks of mathematical concepts built with data from Wikipedia and a collection of scientific papers.
Our approach allows for a unified and intuitive treatment of the structural data (relations between concepts) and functional data (usage of concepts in papers). Since the variance and covariance are general-purpose statistical tools, these new metrics may find application in multiple fields, like neuroscience, economics or social network analysis.