Now showing items 1-20 of 23

• #### A new approach to the spectral excess theorem for distance-regular graphs ﻿

(2009-04-01)
Article
Open Access
The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph $\Gamma$ with $d+1$ different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices.\ The ...
• #### A simple proof of the spectral excess theorem for distance-regular graphs ﻿

(Elsevier, 2010-04-15)
Article
Restricted access - publisher's policy
The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each ...
• #### Betweenness Centrality in Graphs ﻿

(CRC Press Taylor & Francis Group, 2014-10-27)
Part of book or chapter of book
Restricted access - publisher's policy
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. ...
• #### Betweenness-selfcentric graphs ﻿

(2012-04-11)
External research report
Open Access
The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices ...
• #### Boundary value problems for Schrödinger operators on a path ﻿

(2012-05-25)
External research report
Open Access
In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights ...
• #### Boundary value problems for Schrödinger operators on a Path Associated to Orthogonal Polynomials ﻿

(Springer, 2013)
Part of book or chapter of book
Restricted access - publisher's policy
In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights ...
• #### Bounded expansion in models of webgraphs ﻿

(2007-10-02)
Article
Open Access
We study the bounded expansion of several models of web graphs. We show that various deterministic graph models for large complex networks have constant bounded expansion.We study two random models of webgraphs, showing ...
• #### Design of highly synchronizable and robust networks ﻿

(2010-11)
Article
Restricted access - publisher's policy
In this paper, the design of highly synchronizable, sparse and robust dynamical networks is addressed. Better synchronizability means faster synchronization of the oscillators, sparsity means a low ratio of links per ...
• #### Eigenvalue distribution in scale free graphs ﻿

(2007-08-16)
Article
Open Access
Scale free graphs can be found very often as models of real networks and are characterized by a power law degree distribution, that is, for a constant $\gamma\geq 1$ the number of vertices of degree $d$ is proportional ...
• #### Green matrices of weighted graphs with pendant vertices ﻿

(2014)
Lecture
Open Access
• #### Green operators of networks with a new vertex ﻿

(Elsevier, 2016-02)
Article
Open Access
Any elliptic operator defines an automorphism on the orthogonal subspace to the eigenfunctions associated with the lowest eigenvalue, whose inverse is the orthogonal Green operator. In this study, we show that elliptic ...
• #### Green's function of a weighted $n$-cycle ﻿

(2016)
Conference report
Open Access
• #### Group inverse of the laplacian of connections of networks ﻿

(2018-03-25)
External research report
Restricted access - publisher's policy
In previous works the group inverse of a network obtained by some perturbations, as the deletion of a vertex, the addition of a new vertex, contraction of an edge, etc. is obtained in terms of the group inverse of the ...
• #### Jacobi matrices and boundary value problems in distance-regular graphs ﻿

(2012-01-25)
External research report
Open Access
In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain ...
• #### Kirchhoff index of a non-complete wheel ﻿

(2016)
Article
Open Access
In this work, we compute analitycally the Kirchhoff index and effective resistances of a weighted non–complete wheel that has been obtained by adding a vertex to a weighted cycle and some edges conveniently chosen. To this ...
• #### Matriz Laplaciana de grafos ponderados con vértices independientes ﻿

Conference report
Open Access
• #### Notes on betweenness centrality of a graph ﻿

(2009-05-19)
External research report
Open Access
The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. We study selected general properties of this invariant and its relations to ...
• #### On decay centrality in graphs ﻿

(2018-08-06)
Article
Open Access
The decay centrality of a vertex v in a graph G with respect to a parameter d¿(0,1) is a polynomial in d such that for fixed k the coefficient of dk is equal to the number of vertices of G at distance k from v. This invariant ...
• #### On golden spectral graphs ﻿

(2009-03-26)
External research report
Open Access
The concept of golden spectral graphs is introduced and some of their general properties reported. Golden spectral graphs are those having a golden proportion for the spectral ratios defined on the basis of the spectral ...
• #### The betweenness centrality of a graph ﻿

(2007-05-10)
Article
Open Access
A measure of the centrality of a vertex of a graph is the portion of shortest paths crossing through it between other vertices of the graph. This is called betweenness centrality and here we study some of its general ...