Check out the R package diffudist, now also on CRAN! The diffudist package allows you to easily evaluate (and plot with ggplot2) diffusion distances between the nodes of a complex networks and, in so doing, analaysing the functional shape and diffusion geometry of your networks.
In 2017 Manlio De Domenico introduced the family of diffusion distances and induced geometry as a tool for the analysis of the functional organisation of complex networks. Its natural generalisation to multilayer networks was still missing and with this work we filled the gap providing (i) a rigorous mathematical definition of the diffusion distance(s) and induced space(s) in the framework of multilayer networks, (ii) the extension of the diffusion distance definition w.r.t. different random walk dynamics, and (iii) a detailed analysis of the interplay between layer topology, inter-layer connectivity, layer-layer correlations (in terms of edge/partition overlapping), and random walk dynamics.