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Regular version of the site

Ernesto Estrada

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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