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158,326
A note on constructing large Cayley graphs of given degree and diameter by voltage assignments
, 1997
"... Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree and diame ..."
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Cited by 6 (1 self)
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Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 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 ..."
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Cited by 534 (48 self)
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heavy tails for in and outdegree distributions, communities, smallworld phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs
Community detection in graphs
, 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 ..."
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Cited by 801 (1 self)
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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
Large vertextransitive and Cayley graphs with given degree and diameter Abstract
"... We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d = 3m − 1 and diameter k ≥ 3 of order km k. By comparison with other avai ..."
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We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d = 3m − 1 and diameter k ≥ 3 of order km k. By comparison with other
The LargeScale Organization of Metabolic Networks
, 2000
"... In a cell or microorganism the processes that generate mass, energy, information transfer, and cell fate specification are seamlessly integrated through a complex network of various cellular constituents and reactions. However, despite the key role these networks play in sustaining various cellular ..."
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Cited by 599 (7 self)
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and errortolerant networks, and may represent a common blueprint for the largescale organization of interactions among all cellular constituents.
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled
The Digital Michelangelo Project: 3D Scanning of Large Statues
, 2000
"... We describe a hardware and software system for digitizing the shape and color of large fragile objects under nonlaboratory conditions. Our system employs laser triangulation rangefinders, laser timeofflight rangefinders, digital still cameras, and a suite of software for acquiring, aligning, merg ..."
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Cited by 488 (8 self)
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We describe a hardware and software system for digitizing the shape and color of large fragile objects under nonlaboratory conditions. Our system employs laser triangulation rangefinders, laser timeofflight rangefinders, digital still cameras, and a suite of software for acquiring, aligning
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Results 1  10
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