The resistance distance between any two vertices of a graph G is defined as the network
effective resistance between them if each edge of G is replaced by a unit resistor. The …

In a finite irreducible Markov chain with stationary probabilities {π i} and mean first passage
times m ij (mean recurrence time when i= j) it was first shown, by Kemeny and Snell, that is a …

This paper focuses on cascading line failures in the transmission system of the power grid.
Recent large-scale power outages demonstrated the limitations of percolation-and epidemic …

Using a majorization technique that identifies the maximal and minimal vectors of a variety of
subsets of R^ n, we find upper and lower bounds for the Kirchhoff index K (G) of an arbitrary …

We explore the geometry of complex networks in terms of an n-dimensional Euclidean
embedding represented by the Moore–Penrose pseudo-inverse of the graph Laplacian (L+) …

A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by C act
(n; t) the set of connected cacti possessing n vertices and t cycles. In a recent paper (Du et …

Kemeny's constant and its relation to the effective graph resistance has been established for
regular graphs by Palacios et al.[1]. Based on the Moore–Penrose pseudo-inverse of the …

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of
the combinatorial Laplacian matrix (\mathbf L^+) of a simple, undirected graph is proposed …

For an undirected graph, its Kemeny's constant is defined as the mean hitting time of random
walks from one vertex to another chosen randomly according to the stationary distribution …

In this work, we propose a novel robustness measure for networks, which we refer to as
Effective Resistance Centrality of a vertex (or an edge), defined as the relative drop of the …