Graph Rewiring

We define three metrics of the group information power (social capital) in a network based on effective resistance (spectral graph theory). We propose also three metrics of social capital unfairness (structural group unfairness) and a heuristic to mitigate it.

Theoretical and empirical framework to analyze and perform graph rewiring in a principled way. Also, proposal of calulation of Commute Times (resistance) in a GNN layer and Bottleneck minimizarion using Spectral gradients.