DSpace Community:
http://hdl.handle.net/2117/3178
Wed, 01 Apr 2015 13:17:15 GMT2015-04-01T13:17:15Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoAn algorithm to compute the primitive elements of an embedding dimension three numerical semigroups
http://hdl.handle.net/2117/27055
Title: An algorithm to compute the primitive elements of an embedding dimension three numerical semigroups
Authors: Aguiló Gost, Francisco de Asis L.; García Sánchez, Pedro A.; Llena, David
Abstract: We give an algorithm to compute the set of primitive elements for an embedding dimension three numerical semigroups. We show how we use this procedure in the study of the construction of L-shapes and the tame degree of the semigroup.Thu, 26 Mar 2015 11:56:18 GMThttp://hdl.handle.net/2117/270552015-03-26T11:56:18ZAguiló Gost, Francisco de Asis L.; García Sánchez, Pedro A.; Llena, DavidnoNumerical semigroup, L-shapes, primitive elements, tame degreeWe give an algorithm to compute the set of primitive elements for an embedding dimension three numerical semigroups. We show how we use this procedure in the study of the construction of L-shapes and the tame degree of the semigroup.Denumerants of 3-numerical semigroups
http://hdl.handle.net/2117/27054
Title: Denumerants of 3-numerical semigroups
Authors: Aguiló Gost, Francisco de Asis L.; García Sánchez, Pedro A.; Llena, David
Abstract: Denumerants of numerical semigroups are known to be difficult to obtain, even with small embedding dimension of the semigroups. In this work we give some results on denumerants of 3-semigroups S=<a,b,c>S=<a,b,c>. Closed expressions are obtained under certain conditions.Thu, 26 Mar 2015 11:48:29 GMThttp://hdl.handle.net/2117/270542015-03-26T11:48:29ZAguiló Gost, Francisco de Asis L.; García Sánchez, Pedro A.; Llena, DavidnoDenumerant, L-shapes, numerical semigroup, factorizationDenumerants of numerical semigroups are known to be difficult to obtain, even with small embedding dimension of the semigroups. In this work we give some results on denumerants of 3-semigroups S=<a,b,c>S=<a,b,c>. Closed expressions are obtained under certain conditions.Quantum Google algorithm
http://hdl.handle.net/2117/26756
Title: Quantum Google algorithm
Authors: Paparo, Giuseppe Davide; Muller, Markus; Comellas Padró, Francesc de Paula; Martin Delgado, Miguel Angel
Abstract: We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks. The algorithm has been shown to identify unambiguously the underlying topology of the network and to be capable of clearly highlighting the structure of secondary hubs of networks. Furthermore, it can resolve the degeneracy in importance of the low-lying part of the list of rankings. Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks. The quantum algorithm has been shown to display an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance among the nodes, as compared to the classical algorithm.Tue, 17 Mar 2015 12:11:10 GMThttp://hdl.handle.net/2117/267562015-03-17T12:11:10ZPaparo, Giuseppe Davide; Muller, Markus; Comellas Padró, Francesc de Paula; Martin Delgado, Miguel AngelnoPageRank, quantum Google algorithm, complex networksWe review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks. The algorithm has been shown to identify unambiguously the underlying topology of the network and to be capable of clearly highlighting the structure of secondary hubs of networks. Furthermore, it can resolve the degeneracy in importance of the low-lying part of the list of rankings. Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks. The quantum algorithm has been shown to display an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance among the nodes, as compared to the classical algorithm.The number of spanning trees in Apollonian networks
http://hdl.handle.net/2117/26688
Title: The number of spanning trees in Apollonian networks
Authors: Zhang, Zhongzhi; Wu, Bin; Comellas Padró, Francesc de Paula
Abstract: In this paper we find an exact analytical expression for the number of spanning trees in Apollonian networks. This parameter can be related to significant topological and dynamic properties of the networks, including percolation, epidemic spreading, synchronization, and random walks. As Apollonian networks constitute an interesting family of maximal planar graphs which are simultaneously small-world, scale-free, Euclidean and space filling, modular and highly clustered, the study of their spanning trees is of particular relevance. Our results allow also the calculation of the spanning tree entropy of Apollonian networks, which we compare with those of other graphs with the same average degree. (C) 2014 Elsevier B.V. All rights reserved.Fri, 13 Mar 2015 11:07:20 GMThttp://hdl.handle.net/2117/266882015-03-13T11:07:20ZZhang, Zhongzhi; Wu, Bin; Comellas Padró, Francesc de PaulanoApollonian networks, Spanning trees, Small-world graphs, Complex networks, Self-similar, Maximally planar, Scale-free, Complex Networks, Lattices, EnumerationIn this paper we find an exact analytical expression for the number of spanning trees in Apollonian networks. This parameter can be related to significant topological and dynamic properties of the networks, including percolation, epidemic spreading, synchronization, and random walks. As Apollonian networks constitute an interesting family of maximal planar graphs which are simultaneously small-world, scale-free, Euclidean and space filling, modular and highly clustered, the study of their spanning trees is of particular relevance. Our results allow also the calculation of the spanning tree entropy of Apollonian networks, which we compare with those of other graphs with the same average degree. (C) 2014 Elsevier B.V. All rights reserved.The degree/diameter problem in maximal planar bipartite graphs
http://hdl.handle.net/2117/26448
Title: The degree/diameter problem in maximal planar bipartite graphs
Authors: Dalfó Simó, Cristina; Huemer, Clemens; Salas Piñon, Julián
Abstract: The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the (¿; 2) problem, the number of vertices is n = ¿+2; and for the (¿; 3) problem, n = 3¿¿1 if ¿ is odd and n = 3¿ ¿ 2 if ¿ is even. Then, we study the general case (¿;D)
and obtain that an upper bound on n is approximately 3(2D + 1)(¿ ¿ 2)¿D=2¿ and another one is C(¿ ¿ 2)¿D=2¿ if ¿ D and C is a sufficiently large constant. Our upper bound improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (¿ ¿ 2)k if D = 2k, and 3(¿ ¿ 3)k if D = 2k + 1, for ¿ and D sufficiently large in both cases.Fri, 20 Feb 2015 12:42:33 GMThttp://hdl.handle.net/2117/264482015-02-20T12:42:33ZDalfó Simó, Cristina; Huemer, Clemens; Salas Piñon, Juliánno(¿, D) problem, maximal planar bipartite graphsThe (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the (¿; 2) problem, the number of vertices is n = ¿+2; and for the (¿; 3) problem, n = 3¿¿1 if ¿ is odd and n = 3¿ ¿ 2 if ¿ is even. Then, we study the general case (¿;D)
and obtain that an upper bound on n is approximately 3(2D + 1)(¿ ¿ 2)¿D=2¿ and another one is C(¿ ¿ 2)¿D=2¿ if ¿ D and C is a sufficiently large constant. Our upper bound improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (¿ ¿ 2)k if D = 2k, and 3(¿ ¿ 3)k if D = 2k + 1, for ¿ and D sufficiently large in both cases.From clutters to matroids
http://hdl.handle.net/2117/26235
Title: From clutters to matroids
Authors: Martí Farré, JaumeThu, 05 Feb 2015 13:56:31 GMThttp://hdl.handle.net/2117/262352015-02-05T13:56:31ZMartí Farré, Jaumenoclutter, hypergraph, matroid, circuitsFormación interdisciplinar de educación para el desarrollo dirigida a docentes de titulaciones científico-técnicas en un entorno virtual de aprendizaje
http://hdl.handle.net/2117/26103
Title: Formación interdisciplinar de educación para el desarrollo dirigida a docentes de titulaciones científico-técnicas en un entorno virtual de aprendizaje
Authors: Pérez Mansilla, Sonia; BONI, A; Pérez Foguet, Agustí
Abstract: Desde 2001, ISF se ha planteado como estrateg
ia prioritaria para la promoción de la
educación para el desarrollo en la universi
dad, la formación del profesorado de carreras
científico-técnicas. El objeti
vo general es la promoción
de la tecnología para el
desarrollo humano en los estudios de i
ngeniería (Pérez-Foguet et al., 2005).
La estrategia planteada se concretó en
el año 2003 con el cu
rso semipresencial
“Educando en Tecnología para el Desarro
llo”, de 84h de duración y en el que
participaron un total de 61 profesores unive
rsitarios (Boni et al., 2004). En el 2004, se
realizó un taller presencial de
12h titulado “La educación en valores en el ámbito de los
estudios técnicos: el reto del Espaci
o Europeo de Educación Superior”.
Tras estas dos experiencias, se ha realiza
do durante el primer semestre del 2005-06, el
curso interuniversitario semipresencial
“La universidad, instru
mento de solidaridad.
La enseñanza-aprendizaje para el desarrollo humano sostenible en los estudios
científico-técnicos”
, de 125 horas de duración (5 ECTS
) y acreditado por los Institutos
de Ciencias de la Educación de las siguien
tes Universidades: UPM, UPV, UAB, UB y
UPC.
En este artículo se analizará esta acción
formativa desde dos perspectivas: valorando su
relación con el nuevo Espacio Europeo de
Educación Superior y considerando las
posibilidades que ofrece una comunidad virtua
l de aprendizaje formada por expertos y
docentes universitarios.Tue, 27 Jan 2015 11:36:14 GMThttp://hdl.handle.net/2117/261032015-01-27T11:36:14ZPérez Mansilla, Sonia; BONI, A; Pérez Foguet, AgustínoDocentes de titulaciones científico-técnicas
Comunidad virtual de aprendizaje
Educación para el DesarrolloDesde 2001, ISF se ha planteado como estrateg
ia prioritaria para la promoción de la
educación para el desarrollo en la universi
dad, la formación del profesorado de carreras
científico-técnicas. El objeti
vo general es la promoción
de la tecnología para el
desarrollo humano en los estudios de i
ngeniería (Pérez-Foguet et al., 2005).
La estrategia planteada se concretó en
el año 2003 con el cu
rso semipresencial
“Educando en Tecnología para el Desarro
llo”, de 84h de duración y en el que
participaron un total de 61 profesores unive
rsitarios (Boni et al., 2004). En el 2004, se
realizó un taller presencial de
12h titulado “La educación en valores en el ámbito de los
estudios técnicos: el reto del Espaci
o Europeo de Educación Superior”.
Tras estas dos experiencias, se ha realiza
do durante el primer semestre del 2005-06, el
curso interuniversitario semipresencial
“La universidad, instru
mento de solidaridad.
La enseñanza-aprendizaje para el desarrollo humano sostenible en los estudios
científico-técnicos”
, de 125 horas de duración (5 ECTS
) y acreditado por los Institutos
de Ciencias de la Educación de las siguien
tes Universidades: UPM, UPV, UAB, UB y
UPC.
En este artículo se analizará esta acción
formativa desde dos perspectivas: valorando su
relación con el nuevo Espacio Europeo de
Educación Superior y considerando las
posibilidades que ofrece una comunidad virtua
l de aprendizaje formada por expertos y
docentes universitarios.On the ascending subgraph decomposition problem for bipartite graphs
http://hdl.handle.net/2117/26088
Title: On the ascending subgraph decomposition problem for bipartite graphs
Authors: Aroca Farrerons, José María; Lladó Sánchez, Ana M.
Abstract: The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with View the MathML source(n+12) edges admits an edge decomposition G=H1¿¿¿HnG=H1¿¿¿Hn such that HiHi has i edges and is isomorphic to a subgraph of Hi+1Hi+1, i=1,…,n-1i=1,…,n-1. We show that every bipartite graph G with View the MathML source(n+12) edges such that the degree sequence d1,…,dkd1,…,dk of one of the stable sets satisfies di=n-i+2di=n-i+2, 1=i<k1=i<k, admits an ascending subgraph decomposition with star forests. We also give a necessary condition on the degree sequence which is not far from the above sufficient one.Tue, 27 Jan 2015 09:27:34 GMThttp://hdl.handle.net/2117/260882015-01-27T09:27:34ZAroca Farrerons, José María; Lladó Sánchez, Ana M.noAscending subgraph decomposition, Sumset partition problemThe Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with View the MathML source(n+12) edges admits an edge decomposition G=H1¿¿¿HnG=H1¿¿¿Hn such that HiHi has i edges and is isomorphic to a subgraph of Hi+1Hi+1, i=1,…,n-1i=1,…,n-1. We show that every bipartite graph G with View the MathML source(n+12) edges such that the degree sequence d1,…,dkd1,…,dk of one of the stable sets satisfies di=n-i+2di=n-i+2, 1=i<k1=i<k, admits an ascending subgraph decomposition with star forests. We also give a necessary condition on the degree sequence which is not far from the above sufficient one.On perfect and quasiperfect dominations in graphs
http://hdl.handle.net/2117/24831
Title: On perfect and quasiperfect dominations in graphs
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. LuzTue, 25 Nov 2014 10:36:52 GMThttp://hdl.handle.net/2117/248312014-11-25T10:36:52ZCáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. LuznoLD-graphs and global location-domination in bipartite graphs
http://hdl.handle.net/2117/24830
Title: LD-graphs and global location-domination in bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating setS of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD - codes
and the cardinality of an LD-code is the
location-domination number
,
¿
(
G
).
An LD-set
S
of a graph
G
is
global
if it is an LD-set for both
G
and its complement,
G
. One of the main contributions of this work is the definition of the
LD-graph
,an
edge-labeled graph associated to an LD-set, that will be very helpful to deduce some
properties of location-domination in graphs. Concretely, we use LD-graphs to study
the relation between the location-domination number in a bipartite graph and its
complementTue, 25 Nov 2014 10:34:30 GMThttp://hdl.handle.net/2117/248302014-11-25T10:34:30ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuelnodomination, location, complement graph, bipartite graphA dominating setS of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD - codes
and the cardinality of an LD-code is the
location-domination number
,
¿
(
G
).
An LD-set
S
of a graph
G
is
global
if it is an LD-set for both
G
and its complement,
G
. One of the main contributions of this work is the definition of the
LD-graph
,an
edge-labeled graph associated to an LD-set, that will be very helpful to deduce some
properties of location-domination in graphs. Concretely, we use LD-graphs to study
the relation between the location-domination number in a bipartite graph and its
complementThe graph distance game and some graph operations
http://hdl.handle.net/2117/24796
Title: The graph distance game and some graph operations
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
Abstract: In the graph distance game, two players alternate in constructing a max-
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphsFri, 21 Nov 2014 12:24:49 GMThttp://hdl.handle.net/2117/247962014-11-21T12:24:49ZCáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. LuznoDistance game, graph operationsIn the graph distance game, two players alternate in constructing a max-
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphsOn the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes
http://hdl.handle.net/2117/24667
Title: On the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes
Authors: Cámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Abstract: In this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely determined by the local spectra of C. Moreover, we obtain a new characterization for completely pseudo-regular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the spectral excess theorem for extremal sets of vertices. (C) 2013 Elsevier B.V. All rights reserved.Tue, 11 Nov 2014 09:51:20 GMThttp://hdl.handle.net/2117/246672014-11-11T09:51:20ZCámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, ErnestnoPseudo-distance-regularity, Local spectrum, Subconstituents, Predistance polynomials, Completely regular code, GRAPHS, POLYNOMIALSIn this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely determined by the local spectra of C. Moreover, we obtain a new characterization for completely pseudo-regular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the spectral excess theorem for extremal sets of vertices. (C) 2013 Elsevier B.V. All rights reserved.LD-graphs and global location-domination in bipartite graphs
http://hdl.handle.net/2117/24527
Title: LD-graphs and global location-domination in bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S . Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number, ¿(G)¿(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complement, View the MathML sourceG¯. One of the main contributions of this work is the definition of the LD-graph, an edge-labeled graph associated to an LD-set, that will be very helpful to deduce some properties of location-domination in graphs. Concretely, we use LD-graphs to study the relation between the location-domination number in a bipartite graph and its complement.Fri, 31 Oct 2014 12:08:44 GMThttp://hdl.handle.net/2117/245272014-10-31T12:08:44ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuelnodomination, location, complement graph, bipartite graphA dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S . Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number, ¿(G)¿(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complement, View the MathML sourceG¯. One of the main contributions of this work is the definition of the LD-graph, an edge-labeled graph associated to an LD-set, that will be very helpful to deduce some properties of location-domination in graphs. Concretely, we use LD-graphs to study the relation between the location-domination number in a bipartite graph and its complement.The graph distance game and some graph operations
http://hdl.handle.net/2117/24526
Title: The graph distance game and some graph operations
Authors: Cáceres, Jose; Puertas, M. Luz; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exact results for special graphsFri, 31 Oct 2014 12:00:32 GMThttp://hdl.handle.net/2117/245262014-10-31T12:00:32ZCáceres, Jose; Puertas, M. Luz; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoDistance game, graph operationsIn the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exact results for special graphsQuantum Google in a complex network
http://hdl.handle.net/2117/24220
Title: Quantum Google in a complex network
Authors: Paparo, Giuseppe Davide; Muller, Markus; Comellas Padró, Francesc de Paula; Martin Delgado, Miguel Angel
Abstract: We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks.Thu, 02 Oct 2014 17:35:16 GMThttp://hdl.handle.net/2117/242202014-10-02T17:35:16ZPaparo, Giuseppe Davide; Muller, Markus; Comellas Padró, Francesc de Paula; Martin Delgado, Miguel AngelnoComputer science, Information technology, Information theory and computation, Quantum information, Complex networksWe investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks.