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+) …

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 …

Here, we consider a class of generalized linear chains; that is, the ladder‐like chains as a
perturbation of a 2n path by adding consecutive weighted edges between opposite vertices …

Semi-definite positive Schrödinger operators on finite connected networks are particular
examples of a general class of self-adjoint operators called elliptic operators. Any elliptic …

We first present a comprehensive review of various Markov metrics used in the literature and
express them in a consistent framework. We then introduce the fundamental tensor–a …

In electric circuit theory, it is of great interest to compute the effective resistance between any
pair of vertices of a network, as well as the Kirchhoff index. During the past decade these …

A periodic linear chain consists of a weighted 2 n 2 n-path where new edges have been
added following a certain periodicity. In this paper, we obtain the effective resistance and the …

Bounds for the incidence energy of connected bipartite graphs were recently reported. We
now extend these results to connected non-bipartite graphs. In addition, these bounds are …

In this paper we generalize the transition probability matrix for a random walk on a finite
network by defining the transition probabilities through a symmetric M-matrix. Usually, the …

On a finite random walk {X, p (x, y)}, an averaging operator A is defined by A u (x)=∑ p (x, y)
u (y) and its perturbation is A φ u (x)= A u (x)− φ (x) u (x), where φ (x) is a real-valued …