Concentration of the Kirchhoff index for Erdos-Renyi graphs

Understand

Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors.

• Summing these distances over all pairs of nodes yields the so-called Kirchhoff index of the graph, which measures its overall connectivity.
• In this work, we consider Erdos-Renyi random graphs.
• Since the graphs are random, their Kirchhoff indices are random variables.