Sociomeeting: The communicability efficiency

The efficiency of a network was defined by Latora-Marchiori as the average of the inverses of the distances between the nodes. While this definition is rather different than the common understanding of efficiency, it has been proven useful in some applications. However, in many contexts, the shortest distance between two nodes is not necessarily the best one, nor the most economical. As such, some applications are ill-suited for the standard efficiency. As an example, using this definition of efficiency one obtains that randomly rewiring the brain coactivation network results in an efficiency increase. In this talk, I will showcase a stochastic non-conservative model of information spread, the expected value of which coincides with the diffusion model developed by Lerman-Gosh. After showing the model on some toy examples, I will go over an alternative definition of an efficiency measure, based on the average behavior of the model and the communicability distance defined by Estrada. I will continue by explaining what results one obtains when applying this efficiency measure to the brain coactivation network. Finally, I will showcase how, in contrast to the standard efficiency, some edge removals increase the communicability efficiency.