The conjecture that graph conditioning reduces average resistance

Let a graph be conditioned by rescaling its edge weights, and let the resistance distance between two vertices be their effective resistance. Consider the average of this resistance over all distinct pairs of vertices.

Graph-conditioning resistance conjecture. The process of conditioning a graph reduces the average resistance between any two vertices on the graph.

This claim concerns the relationship between spectral conditioning and effective resistance, which is a natural metric on graphs. The supplied text does not state whether the claim has been proved or disproved.