Geometry of complex networks and topological centrality
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+) …
embedding represented by the Moore–Penrose pseudo-inverse of the graph Laplacian (L+) …
A novel measure of edge and vertex centrality for assessing robustness in complex networks
GP Clemente, A Cornaro - Soft Computing, 2020 - Springer
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 …
Effective Resistance Centrality of a vertex (or an edge), defined as the relative drop of the …
Effective resistances for ladder‐like chains
A Carmona, AM Encinas… - International journal of …, 2014 - Wiley Online Library
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 …
perturbation of a 2n path by adding consecutive weighted edges between opposite vertices …
[HTML][HTML] Discrete elliptic operators and their Green operators
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 …
examples of a general class of self-adjoint operators called elliptic operators. Any elliptic …
[HTML][HTML] Markov fundamental tensor and its applications to network analysis
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 …
express them in a consistent framework. We then introduce the fundamental tensor–a …
[HTML][HTML] The Kirchhoff indexes of some composite networks
C Arauz - Discrete Applied Mathematics, 2012 - Elsevier
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 …
pair of vertices of a network, as well as the Kirchhoff index. During the past decade these …
Kirchhoff index of periodic linear chains
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 …
added following a certain periodicity. In this paper, we obtain the effective resistance and the …
[PDF][PDF] Estimating the incidence energy
SB Bozkurt, I Gutman - MATCH Commun. Math. Comput. Chem, 2013 - match.pmf.kg.ac.rs
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 …
now extend these results to connected non-bipartite graphs. In addition, these bounds are …
[HTML][HTML] Random walks associated with symmetric M-matrices
A Carmona, AM Encinas, MJ Jimenez… - Linear Algebra and its …, 2024 - Elsevier
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 …
network by defining the transition probabilities through a symmetric M-matrix. Usually, the …
A perturbed averaging operator on finite graphs
VR Manivannan, V Anandam - Linear Algebra and its Applications, 2024 - Elsevier
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 …
u (y) and its perturbation is A φ u (x)= A u (x)− φ (x) u (x), where φ (x) is a real-valued …