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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

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
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

Efficient graph-based image segmentation.

by Pedro F Felzenszwalb , Daniel P Huttenlocher - International Journal of Computer Vision, , 2004
"... Abstract. This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show ..."
Abstract - Cited by 940 (1 self) - Add to MetaCart
that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm

Secure Group Communications Using Key Graphs

by Chung Kei Wong, Mohamed Gouda , Simon S. Lam - SIGCOMM '98 , 1998
"... Many emerging applications (e.g., teleconference, real-time information services, pay per view, distributed interactive simulation, and collaborative work) are based upon a group communications model, i.e., they require packet delivery from one or more authorized senders to a very large number of au ..."
Abstract - Cited by 556 (17 self) - Add to MetaCart
Many emerging applications (e.g., teleconference, real-time information services, pay per view, distributed interactive simulation, and collaborative work) are based upon a group communications model, i.e., they require packet delivery from one or more authorized senders to a very large number

A Critical Point For Random Graphs With A Given Degree Sequence

by Michael Molloy, Bruce Reed , 2000
"... Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
Abstract - Cited by 507 (8 self) - Add to MetaCart
Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0

Scalable modeling of real graphs using Kronecker multiplication

by Jure Leskovec, Christos Faloutsos - IN 24TH ICML , 2007
"... Given a large, real graph, how can we generate a synthetic graph that matches its properties, i.e., it has similar degree distribution, similar (small) diameter, similar spectrum, etc? We propose to use “Kronecker graphs”, which naturally obey all of the above properties, and we present KronFit, a f ..."
Abstract - Cited by 72 (9 self) - Add to MetaCart
Given a large, real graph, how can we generate a synthetic graph that matches its properties, i.e., it has similar degree distribution, similar (small) diameter, similar spectrum, etc? We propose to use “Kronecker graphs”, which naturally obey all of the above properties, and we present KronFit, a

Statistical mechanics of complex networks

by Réka Albert, Albert-lászló Barabási - 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 ..."
Abstract - Cited by 2148 (11 self) - Add to MetaCart
as random graphs, it is increasingly recognized that the topology and evolution of real

Finding community structure in networks using the eigenvectors of matrices

by M. E. J. Newman , 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average 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 ..."
Abstract - Cited by 502 (0 self) - Add to MetaCart
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

A theory of timed automata

by Rajeev Alur , 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
Abstract - Cited by 2651 (32 self) - Add to MetaCart
of real-time systems whose correctness depends on relative magnitudes of different delays. Consequently, timed automata [7] were introduced as a formal notation to model the behavior of real-time systems. Its definition provides a simple way to annotate state-transition graphs with timing constraints

Gradient-based learning applied to document recognition

by Yann Lecun, Léon Bottou, Yoshua Bengio, Patrick Haffner - Proceedings of the IEEE , 1998
"... Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradientbased learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify hi ..."
Abstract - Cited by 1533 (84 self) - Add to MetaCart
to deal with the variability of two dimensional (2-D) shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation, recognition, and language modeling. A new learning paradigm, called graph
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