We prove a relationship between the isoperimetric number, Cheeger constant, and second-smallest eigenvalue of the normalized Laplacian of a graph $G$ and its complement $G^c$.
We extend the definition of Kemeny’s constant to non-backtracking random walks and explore its relationship to the simple random walk.
We prove a new identity for Kemeny’s constant and provide sufficient conditions for an edge to be Braess in a general class of graphs.
We obtain generalized formulas for the resistance distance and other graph metrics for a new class of graphs.