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Sizes of graphs with fixed ordered and spans for circulardistancetwo labelings
 Ars Combin
"... A kcirculardistancetwo labeling (or kclabeling) of a simple graph G is a vertexlabeling, using the labels 0, 1, 2, · · · , k − 1, such that the “circular difference” (mod k) of the labels for adjacent vertices is at least two, and for vertices of distancetwo apart is at least one. The σnu ..."
Abstract

Cited by 1 (0 self)
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that for any value p between the maximum and the minimum size, there exists a graph G ∈ G σ (n, k) of size p. These results are analogues of the ones by Georges and Mauro [4] on distancetwo labelings. Keywords. Vertexlabeling, circular difference, circulardistancetwo labeling, distancetwo labeling. 1
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
LabelMe: A Database and WebBased Tool for Image Annotation
, 2008
"... We seek to build a large collection of images with ground truth labels to be used for object detection and recognition research. Such data is useful for supervised learning and quantitative evaluation. To achieve this, we developed a webbased tool that allows easy image annotation and instant sha ..."
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Cited by 670 (47 self)
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recognition and detection. Also, we show how to extend the dataset to automatically enhance object labels with WordNet, discover object parts, recover a depth ordering of objects in a scene, and increase the number of labels using minimal user supervision and images from the web.
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
The Architecture of Cognition
, 1983
"... Spanning seven orders of magnitude: a challenge for ..."
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Cited by 1580 (40 self)
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Spanning seven orders of magnitude: a challenge for
The program dependence graph and its use in optimization
 ACM Transactions on Programming Languages and Systems
, 1987
"... In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program. ..."
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Cited by 989 (3 self)
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In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program
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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, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should
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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as random graphs, it is increasingly recognized that the topology and evolution of real
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