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COMPTHE  Combinatorial Theory and Discrete Potential parameters for control networks
VARIDIS  Discrete Riemannian Manifolds and Potential Theory  Department
 Department of Applied Mathematics III
 School
 Escola Universitària d'Enginyeria Tècnica Industrial de Barcelona (EUETIB)
 silvia.gagoupc.edu
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Scientific and technological production


On betweennessuniform graphs
Gago Alvarez, Silvia; Coronicová Hurajová, Jana; Madaras, Tomas
Czechoslovak mathematical journal
Date of publication: 201309
Journal article
Read the abstract View Share Reference managersThe betweenness centrality of a vertex of a graph is the fraction of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices have the same value of betweenness centrality (betweennessuniform graphs); we show that this property holds for distanceregular graphs (which include strongly regular graphs) and various graphs obtained by graph cloning and local join operation. In addition, we show that, for sufficiently large $n$, there are superpolynomially many betweennessuniform graphs on $n$ vertices, and explore the structure of betweennessuniform graphs having a universal or subuniversal vertex. 
Review MR2882891 a Mathscinet
Gago Alvarez, Silvia
Date: 2013
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Boundary value problems for Schrödinger operators on a Path Associated to Orthogonal Polynomials
Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
Date of publication: 2013
Book chapter
Read the abstract View Share Reference managersIn 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 are determined by the coefficients of the threeterm recurrence relation.
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 are determined by the coefficients of the threeterm recurrence relation. 
Tree forest metrics for Schrödinger operators in networks
Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
CzechSlovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications
Presentation's date: 20130712
Presentation of work at congresses
Read the abstract View Share Reference managersMetrics in graphs provide measures of proximity between vertices. The classical shortpath distances can be replaced for more general metrics, as the adjusted forest metric introduced by Chebotarev et al. in [2]. Other related distance is the one provided for the resistance distance of a network [3]. The objective of our work is to generalize the adjusted forest metric related to Laplacian operators to the adjusted forest metric related to Schr¨odinger operators, under the functional analysis framework. Furthermore, we show that it can be computed in terms ofthe effective resistances of the network. 
Boundary value problems on a weighted path
Gago Alvarez, Silvia; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
Midsummer Combinatorial Workshop
Presentation's date: 20130801
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Read the abstract View Share Reference managersIn this work we solve usual boundary value problems on a weighted path via orthogonal polynomials 
Notes on the betweenness centrality of a graph
Gago Alvarez, Silvia; Hurajová, Jana; Madaras, Tomas
Mathematica slovaca
Date of publication: 20120101
Journal article
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Jacobi matrices and boundary value problems in distanceregular graphs
Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
Electronic journal of linear algebra
Date of publication: 201211
Journal article
Read the abstract View Share Reference managersRegular boundary value problems on a distanceregular graph associated with Schrodinger operators are analyzed. These problems include the cases in which the boundary has one or two vertices. In each case, the Green matrices are given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distanceregular graphs. 
Review MR2883831 a Mathscinet
Gago Alvarez, Silvia
Date: 20120815
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Review MR2881990 a Mathscinet
Gago Alvarez, Silvia
Date: 2012
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Review MR2867609 a Mathscinet
Gago Alvarez, Silvia
Date: 20120616
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Boundary value problems for Schrödinger operators on a path
Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
Date: 20120525
Report
Read the abstract Access to the full text Share Reference managersIn 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 are determined by the coefficients of the three terms recurrence relation defining the polynomials. Our study is similar to what is known for boundary value problems associated with ordinary differential equations. 
Betweennessselfcentric graphs
Gago Alvarez, Silvia; Hurajová, Jana; Madaras, Tomas
Date: 20120411
Report
Read the abstract Access to the full text Share Reference managersThe 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 have the same value of betweenness centrality. 
Review MR2737127 a Mathscinet
Gago Alvarez, Silvia
Date: 2012
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Jacobi matrices and boundary value problems in distanceregular graphs
Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
Date: 20120125
Report
Read the abstract Access to the full text Share Reference managersIn this work we analyze regular boundary value problems on a distanceregular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distanceregular graphs. 
Control de invariantes en grafos sujetos a propiedades estructurales
Marcote Ordax, Francisco Javier; Salas Piñon, Julian; Hansberg Pastor, Adriana; Cera, Martín; Gago Alvarez, Silvia; Balbuena Martinez, Maria Camino Teofila
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Twoside boundary value problems in distanceregular graphs
Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 20120713
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersIn this work we analyze regular boundary value problems on a distanceregular graph associated with Schr¨odinger operators in the case that the boundary has two vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrix is given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distanceregular graph. 
Boundary value problems in distanceregular graphs
Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
International Workshop on Optimal Network Topologies
Presentation's date: 20120728
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Review MR2659419 (2011i:90014) a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Review MR2816660 a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Review MR2666293 (2011g:90040) a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Review MR2833618 a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Review MR2721750 (2011j:05092) a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Review MR2742371 (2012a:37105) a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Review MR2809028 a Mathscinet
Gago Alvarez, Silvia
Date: 2011
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Problemas de contorno discretos y técnicas de aproximación en estados de equilibrio
Arauz Lombardia, Cristina; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia; Medina Sierra, Agustin; Bendito Perez, Enrique
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On betweennessselfcentric graphs
Gago Alvarez, Silvia; Hurajová, Jana; Madaras, Tomas
20th Workshop '3in1'
Presentation's date: 20111124
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Schrödinger operators and boundary value problems in a path associated to orthogonal polynomials
Gago Alvarez, Silvia
International Conference on Differential & Difference Equations and Applications
Presentation's date: 20110704
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Spectral Techniques in Complex Networks
Gago Alvarez, Silvia
Date of publication: 201101
Book chapter
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Jacobi matrices and boundary value problems in distance regular graphs
Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
Directions in Matrix Theory
Presentation's date: 20110709
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Design of highly synchronizable and robust networks
Estrada Roger, Ernesto; Gago Alvarez, Silvia; Caporossi, Gilles
Automatica
Date of publication: 201011
Journal article
Read the abstract View Share Reference managersIn 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 nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes/links. Golden spectral dynamical networks (graphs) are those for which the spectral spread (the difference between the largest and smallest eigenvalues of the adjacency matrix) is equal to the spectral gap (the difference between the two largest eigenvalues of the adjacency matrix) multiplied by the square of the golden ratio. These networks display the property of ‘‘smallworldness’’, are very homogeneous and have large isoperimetric (expansion) constant, together with a very high synchronizability and robustness to failures of individual oscillators. In particular, the regular bipartite dynamical networks, reported here by the first time, have the best possible expansion and consequently are the most robust ones against node/link failures or intentional attacks. 
A simple proof of the spectral excess theorem for distanceregular graphs
Fiol Mora, Miquel Àngel; Gago Alvarez, Silvia; Garriga Valle, Ernest
Linear algebra and its applications
Date of publication: 20100415
Journal article
Read the abstract View Share Reference managersThe spectral excess theorem provides a quasispectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distanceregular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the socalled pseudodistanceregularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role. 
Review MR2558969 (2011d:05231) a Mathscinet
Gago Alvarez, Silvia
Date: 2010
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Review MR2577712 (2011d:05216) a Mathscinet
Gago Alvarez, Silvia
Date: 2010
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Diseño de redes altamente sincronizables y robustas
Caporossi, Gilles; Estrada Roger, Ernesto; Gago Alvarez, Silvia
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 20100707
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Bounded expansion in web graphs
Gago Alvarez, Silvia; Schlatter, Dirk
Commentationes Mathematicae Universitatis Carolinae
Date of publication: 2009
Journal article
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Fonaments matemàtics per a l'enginyeria de telecomunicació
Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Gago Alvarez, Silvia; Heymann Pignolo, Marco; Tramuns Figueras, Eulalia
Date of publication: 200907
Book
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On golden spectral graphs
Gago Alvarez, Silvia; Estrada Roger, Ernesto
Date: 20090326
Report
Read the abstract Access to the full text Share Reference managersThe 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 gap, spectral spread and the difference between the second largest and the smallest eigenvalue of the adjacency matrix. They are good expanders and display excellent synchronizability. Here we report some new construction methods as well as several of their topological parameters. 
COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS
Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Espona Dones, Margarida; Rius Font, Miquel; Aroca Farrerons, Josep Maria; Aguilo Gost, Francisco de Asis Luis; Dalfo Simo, Cristina; Moragas Vilarnau, Jordi; Cámara Vallejo, Marc; Gago Alvarez, Silvia; Ball, Simeon Michael; Andres Yebra, Jose Luis; Pérez Mansilla, Sonia; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Fàbrega Canudas, Josep; Muñoz Lopez, Francisco Javier; Zaragoza Monroig, Maria Luisa; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
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PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC
Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
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On Golden Spectral Graphs
Gago Alvarez, Silvia; Estrada Roger, Ernesto
British Combinatorial Conference
Presentation's date: 20090708
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThe 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 gap, spectral spread and the difference between the second largest and the smallest eigenvalue of the adjacency matrix. They are good expanders and display excellent synchronizability. Here we report some new construction methods as well as several of their topological parameters. 
Eigenvalue distribution in power law graphs
Gago Alvarez, Silvia
Aplimat journal of applied mathematics
Date of publication: 200802
Journal article
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Eigenvalue distribution in power law graphs
Gago Alvarez, Silvia
The 7th International Conference on Applied Mathematics Aplimat 2008
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Expansión acotada en grafos que modelan la World Wide Web
Gago Alvarez, Silvia; Schlatter, D
Jornadas de Matemática Discreta y Algorítmica
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A new Approach to the Spectral Excess Theorem for DistanceRegular Graphs
Gago Alvarez, Silvia; Garriga Valle, Ernest; Fiol Mora, Miquel Àngel
Workshop on Spectral Graph Theory with applications on Computer Science, Combinatorial Optimization and Chemistry
Presentation's date: 20081201
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThe Spectral Excess Theorem provides a quasispectral characterization for a (regular) graph $\Gamma$ with $d+1$ different eigenvalues to be distanceregular graph, in terms of the mean (d1)excess of its vertices.\ The original approach, due to Fiol and Garriga in $1997$, was obtained in a wide context from a local point of view, so giving a characterization of the socalled pseudodistanceregularity around a vertex.\ In this paper we present a new simple method based in a global point of view, and where the mean degree of the distance$d$ graph $\Gamma_d$ plays an essential role. 
The betweenness centrality of a graph
Gago Alvarez, Silvia
Date: 200705
Report
Read the abstract Access to the full text Share Reference managersA 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 properties, relations with distance parameters (diameter, mean distance), local parameters, symmetries, etc. Some bounds for this parameter are obtained, using them to improve known bounds for the mean distance of the graph. 
Eigenvalue distribution in scale free graphs
Gago Alvarez, Silvia
Date: 200708
Report
Read the abstract Access to the full text Share Reference managersScale 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 to $d^{\gamma}$. Experimental studies show that the eigenvalue distribution also follows a power law for the highest eigenvalues. Hence it has been conjectured that the power law of the degrees determines the power law of the eigenvalues. In this paper we show that we can construct a scale free graph with non highest eigenvalue power law distribution. For $\gamma=1$ we can construct a scale free graph with small spectrum and a regular graph with eigenvalue power law distribution. 
Bounded expansion in models of webgraphs
Gago Alvarez, Silvia; Schlatter, D
Date: 200710
Report
Read the abstract Access to the full text Share Reference managersWe 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 that the model of Bonato has not bounded expansion, and we conjecture that the classical model of Barabási may have also not bounded expansion. 
Spectral bounds for the betweenness of a graph
Comellas Padro, Francesc de Paula; Gago Alvarez, Silvia
Linear algebra and its applications
Date of publication: 200705
Journal article
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Synchronizability of complex networks
Comellas Padro, Francesc de Paula; Gago Alvarez, Silvia
Journal of physics A. Mathematical and theoretical
Date of publication: 200704
Journal article
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Vertex Betweenness centrality in graphs
Gago Alvarez, Silvia
British Combinatorial Conference
Presentation's date: 20070711
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