Results 1  10
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23
On the Eigenvalue Power Law
, 2002
"... We show that the largest eigenvalues of graphs whose highest degrees are Zipflike distributed with slope are distributed according to a power law with slope =2. This follows as a direct and almost certain corollary of the degree power law. Our result has implications for the singular value deco ..."
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Cited by 50 (0 self)
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We show that the largest eigenvalues of graphs whose highest degrees are Zipflike distributed with slope are distributed according to a power law with slope =2. This follows as a direct and almost certain corollary of the degree power law. Our result has implications for the singular value decomposition method in information retrieval.
ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
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Cited by 27 (10 self)
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vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
A Theorem about the Channel Assignment Problem
, 2001
"... A list channel assignment problem is a triple (G, L, w) where G is a graph, L is a function assigning vertices of G lists of integers (colours) and w is a function assigning edges of G positive integers (weights). A colouring c of the vertices of G is proper if c(v) ∈ L(v) for each vertex v and ..."
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Cited by 26 (7 self)
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A list channel assignment problem is a triple (G, L, w) where G is a graph, L is a function assigning vertices of G lists of integers (colours) and w is a function assigning edges of G positive integers (weights). A colouring c of the vertices of G is proper if c(v) ∈ L(v) for each vertex v and c(u)c(v) ≥ w(uv) for each edge uv. A weighted degree deg_w(v) of a vertex v is the sum of the weights of the edges incident with v. If G is connected, L(v) > deg_w(v) for at least one v and L(v) ≥ deg_w(v) for all v, then a proper colouring always exists.
Robustness as an Evolutionary Principle
 Proceedings of the Royal Society of London, Series B
, 2000
"... We suggest simulating evolution of complex organisms using... ..."
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Cited by 18 (1 self)
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We suggest simulating evolution of complex organisms using...
Updating the hamiltonian problem  a survey
 J. Graph Theory
, 1991
"... This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs. 1 ..."
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Cited by 17 (0 self)
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This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs. 1
Coevolution of social and affiliation networks
 In 15th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD
, 2009
"... In our work, we address the problem of modeling social network generation which explains both link and group formation. Recent studies on social network evolution propose generative models which capture the statistical properties of realworld networks related only to nodetonode link formation. We ..."
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Cited by 16 (1 self)
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In our work, we address the problem of modeling social network generation which explains both link and group formation. Recent studies on social network evolution propose generative models which capture the statistical properties of realworld networks related only to nodetonode link formation. We propose a novel model which captures the coevolution of social and affiliation networks. We provide surprising insights into group formation based on observations in several realworld networks, showing that users often join groups for reasons other than their friends. Our experiments show that the model is able to capture both the newly observed and previously studied network properties. This work is the first to propose a generative model which captures the statistical properties of these complex networks. The proposed model facilitates controlled experiments which study the effect of actors ’ behavior on the network evolution, and it allows the generation of realistic synthetic datasets.
Random biochemical networks: the probability of selfsustaining autocatalysis
 Journal of Theoretical Biology
, 2004
"... ..."
Small Worlds  The Structure of Social Networks
, 1999
"... Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the six degrees of separation, has been the subject of a conside ..."
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Cited by 14 (2 self)
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Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the six degrees of separation, has been the subject of a considerable amount of recent research and modeling, which we review here.
On the Representation and Multiplication of Hypersparse Matrices
, 2008
"... Multicore processors are marking the beginning of a new era of computing where massive parallelism is available and necessary. Slightly slower but easy to parallelize kernels are becoming more valuable than sequentially faster kernels that are unscalable when parallelized. In this paper, we focus on ..."
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Cited by 9 (7 self)
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Multicore processors are marking the beginning of a new era of computing where massive parallelism is available and necessary. Slightly slower but easy to parallelize kernels are becoming more valuable than sequentially faster kernels that are unscalable when parallelized. In this paper, we focus on the multiplication of sparse matrices (SpGEMM). We first present the issues with existing sparse matrix representations and multiplication algorithms that make them unscalable to thousands of processors. Then, we develop and analyze two new algorithms that overcome these limitations. We consider our algorithms first as the sequential kernel of a scalable parallel sparse matrix multiplication algorithm and second as part of a polyalgorithm for SpGEMM that would execute different kernels depending on the sparsity of the input matrices. Such a sequential kernel requires a new data structure that exploits the hypersparsity of the individual submatrices owned by a single processor after the 2D partitioning. We experimentally evaluate the performance and characteristics of our algorithms and show that they scale significantly better than existing kernels.
Random walks on wreath products of groups
 MR 2003f:60018
"... We bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G ≀ Sn for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the hyperoctahedral group Z2 ≀ Sn, the generalized symmetric group Zm ≀ Sn, a ..."
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Cited by 7 (1 self)
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We bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G ≀ Sn for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the hyperoctahedral group Z2 ≀ Sn, the generalized symmetric group Zm ≀ Sn, and Sm ≀ Sn. These results provide benchmarks to which many other random walks, modeling a wide range of phenomena, may be compared using the comparison technique, thereby yielding bounds on the rates of convergence to uniformity for previously intractable random walks. 1. Introduction. How