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Community detection in graphs

by Santo Fortunato , 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
Abstract - Cited by 821 (1 self) - Add to MetaCart
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices

Algebraic Graph Theory

by Chris Godsil, Mike Newman , 2011
"... 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 ..."
Abstract - Cited by 892 (13 self) - Add to MetaCart
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

An algorithm for drawing general undirected graphs

by Tomihisa Kamada, Satoru Kawai - Information Processing Letters , 1989
"... Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, data-flow graphs, Petri nets, and entit ..."
Abstract - Cited by 698 (2 self) - Add to MetaCart
Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, data-flow graphs, Petri nets

High dimensional graphs and variable selection with the Lasso

by Nicolai Meinshausen, Peter Bühlmann - ANNALS OF STATISTICS , 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
Abstract - Cited by 736 (22 self) - Add to MetaCart
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso

Graph-based algorithms for Boolean function manipulation

by Randal E. Bryant - IEEE TRANSACTIONS ON COMPUTERS , 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
Abstract - Cited by 3526 (46 self) - Add to MetaCart
In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions

Fast Planning Through Planning Graph Analysis

by Avrim L. Blum, Merrick L. Furst - ARTIFICIAL INTELLIGENCE , 1995
"... We introduce a new approach to planning in STRIPS-like domains based on constructing and analyzing a compact structure we call a Planning Graph. We describe a new planner, Graphplan, that uses this paradigm. Graphplan always returns a shortest possible partial-order plan, or states that no valid pla ..."
Abstract - Cited by 1171 (3 self) - Add to MetaCart
We introduce a new approach to planning in STRIPS-like domains based on constructing and analyzing a compact structure we call a Planning Graph. We describe a new planner, Graphplan, that uses this paradigm. Graphplan always returns a shortest possible partial-order plan, or states that no valid

Efficiently computing static single assignment form and the control dependence graph

by Ron Cytron, Jeanne Ferrante, Barry K. Rosen, Mark N. Wegman, F. Kenneth Zadeck - ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS , 1991
"... In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single ass ..."
Abstract - Cited by 1003 (8 self) - Add to MetaCart
assignment form and the control dependence graph have been proposed to represent data flow and control flow propertiee of programs. Each of these previously unrelated techniques lends efficiency and power to a useful class of program optimization. Although both of these structures are attractive

Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations

by Jure Leskovec, Jon Kleinberg, Christos Faloutsos , 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
Abstract - Cited by 541 (48 self) - Add to MetaCart
, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.

The structure and function of complex networks

by M. E. J. Newman - SIAM REVIEW , 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
Abstract - Cited by 2600 (7 self) - Add to MetaCart
, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Convolution Kernels on Discrete Structures

by David Haussler , 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
Abstract - Cited by 506 (0 self) - Add to MetaCart
We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes
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