“Communicability functions and geometrical properties of networks ”
Recent interest in geometric properties of networks has triggered research on embedding graphs on certain geometric spaces. Our approach follows a different route as it finds the geometry induced by functions of the adjacency matrix of networks, known as communicability functions. In this talk I will motivate the necessity for characterizing the spatial efficiency of networks. Then, I will show how matrix functions defining the communicability among nodes in a network induces an embedding into high- dimensional Euclidean spaces, which allow us to characterize the spatial efficiency of graphs. We will define a communicability distance function and the corresponding Euclidean angles between the position vectors of the nodes in the induced embedding. I will show examples of applications of these concepts to characterize the spatial efficiency of networks as well as some dynamical processes taking place on them.
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