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Efficient Testing of Large Graphs
 Combinatorica
"... Let P be a property of graphs. An test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case that it h ..."
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Cited by 187 (49 self)
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Let P be a property of graphs. An test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case
Pregel: A system for largescale graph processing
 IN SIGMOD
, 2010
"... Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model ..."
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Cited by 472 (0 self)
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Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational
Clustering in Large Graphs and Matrices
, 1999
"... We consider the problem of dividing a set of m points in Euclidean n\Gammaspace into k clusters (m; n are variable while k is fixed), so as to minimize the sum of distance squared of each point to its "cluster center". This formulation differs in two ways from the most frequently considere ..."
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Cited by 105 (26 self)
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We consider the problem of dividing a set of m points in Euclidean n\Gammaspace into k clusters (m; n are variable while k is fixed), so as to minimize the sum of distance squared of each point to its "cluster center". This formulation differs in two ways from the most frequently considered clustering problems in the literature, namely, here we have k fixed and m;n variable and we use the sum of squared distances as our measure; we will argue that our problem is natural in many contexts. We consider a relaxation of the discrete problem : find the k\Gammadimensional subspace V so that the sum of distances squared to V (of the m points) is minimized. We show : (i) The relaxation can be solved by Singular Value Decomposition (SVD) of Linear Algebra. (ii) The solution of the relaxation can be used to get a 2approximation algorithm for the original problem. More importantly, (iii) we argue that in fact the relaxation provides a generalized clustering which is useful in its own right. Final...
An improved algorithm for matching large graphs
 In: 3rd IAPRTC15 Workshop on Graphbased Representations in Pattern Recognition, Cuen
, 2001
"... In this paper an improved version of a graph matching algorithm is presented, which is able to efficiently solve the graph isomorphism and graphsubgraph isomorphism problems on Attributed Relational Graphs. This version is particularly suited to work with very large graphs, since its memory require ..."
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Cited by 96 (4 self)
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In this paper an improved version of a graph matching algorithm is presented, which is able to efficiently solve the graph isomorphism and graphsubgraph isomorphism problems on Attributed Relational Graphs. This version is particularly suited to work with very large graphs, since its memory
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
On the Vulnerability of Large Graphs
"... Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k node ..."
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Cited by 26 (11 self)
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Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k
Sampling from Large Graphs
"... Given a huge real graph, how can we derive a representative sample? There are many known algorithms to compute interesting measures (shortest paths, centrality, betweenness, etc.), but several of them become impractical for large graphs. Thus graph sampling is essential. ..."
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Given a huge real graph, how can we derive a representative sample? There are many known algorithms to compute interesting measures (shortest paths, centrality, betweenness, etc.), but several of them become impractical for large graphs. Thus graph sampling is essential.
Algebraic Graph Theory
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 868 (12 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Accelerating large graph algorithms on the GPU using CUDA
"... Abstract. Graph algorithms are fundamental to many disciplines and application areas. Large graphs involving millions of vertices are common in scientific and engineering applications. Practicaltime implementations using highend computing resources have been reported but are accessible only to a f ..."
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Cited by 149 (5 self)
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Abstract. Graph algorithms are fundamental to many disciplines and application areas. Large graphs involving millions of vertices are common in scientific and engineering applications. Practicaltime implementations using highend computing resources have been reported but are accessible only to a
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