An explicit link between graphical models and Gaussian Markov random fields on metric graphs
We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a Gaussian graphical model. This graphical model has a distribution which is faithful to its pairwise independence graph, that coincides with the neighbor structure of
