Graphs and Networks in Hyperspheres
Presented by Prof. Estrada ERNESTO
Type: Keynote Lecture
The concept of communicability between pairs of nodes in a graph is introduced. Then, the communicability distance is defined and it is proved that it corresponds to a Euclidean distance in the graph. The mathematical expressions for the communicability distance between pairs of nodes in paths, cycles, stars and complete graphs are obtained as well as the expressions for the sum of all distances in these graphs. The consequences of using the communicability distance in real-world complex networks is analyzed. Finally, we prove that the communicability distance induces an embedding of the graph into a high-dimensional sphere (hypersphere). We finally show some applications of the ratio of surface area to volume for these hyperspheres in real-world networks.