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On the Evolution of Random Graphs
 PUBLICATION OF THE MATHEMATICAL INSTITUTE OF THE HUNGARIAN ACADEMY OF SCIENCES
, 1960
"... his 50th birthday. Our aim is to study the probable structure of a random graph rn N which has n given labelled vertices P, P2,..., Pn and N edges; we suppose_ ..."
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Cited by 1849 (7 self)
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his 50th birthday. Our aim is to study the probable structure of a random graph rn N which has n given labelled vertices P, P2,..., Pn and N edges; we suppose_
Characterization of complex networks: A survey of measurements
 Advances in Physics
"... Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of mea ..."
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Cited by 89 (7 self)
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Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the
The Birth of the Giant Component
, 1993
"... Limiting distributions are derived for the sparse connected components that are present when a random graph on n vertices has approximately 1 n edges. In particular, we show that such a graph consists entirely of trees, 2 unicyclic components, and bicyclic components with probability approaching ..."
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Cited by 31 (5 self)
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Limiting distributions are derived for the sparse connected components that are present when a random graph on n vertices has approximately 1 n edges. In particular, we show that such a graph consists entirely of trees, 2 unicyclic components, and bicyclic components with probability approaching
HADI: Mining radii of large graphs
 ACM Transactions on Knowledge Discovery from Data
, 2010
"... Given large, multimillion node graphs (e.g., Facebook, webcrawls, etc.), how do they evolve over time? How are they connected? What are the central nodes and the outliers? In this paper we define the Radius plot of a graph and show how it can answer these questions. However, computing the Radius p ..."
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Cited by 16 (8 self)
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Given large, multimillion node graphs (e.g., Facebook, webcrawls, etc.), how do they evolve over time? How are they connected? What are the central nodes and the outliers? In this paper we define the Radius plot of a graph and show how it can answer these questions. However, computing the Radius plot is prohibitively expensive for graphs reaching the planetary scale. There are two major contributions in this paper: (a) We propose HADI (HAdoop DIameter and radii estimator), a carefully designed and finetuned algorithm to compute the radii and the diameter of massive graphs, that runs on the top of the Hadoop/MapReduce system, with excellent scaleup on the number of available machines (b) We run HADI on several real world datasets including YahooWeb (6B edges, 1/8 of a Terabyte), one of the largest public graphs ever analyzed. Thanks to HADI, we report fascinating patterns on large networks, like the surprisingly small effective diameter, the multimodal/bimodal shape of the Radius plot, and its palindrome motion over time.
Information Flow Structure in LargeScale Product Development Organizational Networks
 TO APPEAR IN SMART BUSINESS NETWORKS, PETER VERVEST ET AL (EDS), SPRINGER VERLAG.
, 2004
"... ..."
Local learning to improve organizational performance in networked multiagent team formation
 In Proceedings of the AAAI 05 Workshop on MultiAgent Learning
, 2005
"... Networked multiagent systems are comprised of many autonomous yet interdependent agents situated in a virtual social network. Two examples of such systems are supply chain networks and sensor networks. A common challenge in many networked multiagent systems is decentralized team formation among the ..."
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Cited by 1 (0 self)
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Networked multiagent systems are comprised of many autonomous yet interdependent agents situated in a virtual social network. Two examples of such systems are supply chain networks and sensor networks. A common challenge in many networked multiagent systems is decentralized team formation among the spatially and logically extended agents. Even in cooperative multiagent systems, efficient team formation is made difficult by the limited local information available to the individual agents. We present a model of distributed multiagent team formation in networked multiagent systems, describe a policy learning framework for joining teams based on local information, and give empirical results on improving team formation performance. In particular, we show that local policy learning from limited information leads to a significant increase in organizational team formation performance compared to a naive heuristic.
Analyzing Protein Interaction Networks via Random Graph Model
, 2005
"... Many complex systems may best be described as networks, which we can use graph theory to analyze their topological properties. In an organism, proteinprotein interactions may also be mapped into complex network. Here we use random graph theory to analyze seven different organism protein interaction ..."
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Many complex systems may best be described as networks, which we can use graph theory to analyze their topological properties. In an organism, proteinprotein interactions may also be mapped into complex network. Here we use random graph theory to analyze seven different organism protein interaction networks. Three topological properties (degree distribution, clustering coefficient and average shortest path) were used to characterize these networks. The logarithm of the node degree distribution vs. the logarithm of the node degree plot shows that all seven species follow a powerlaw distribution quite well. In addition, we also obtained the relatively high clustering coefficient of these protein interaction networks. The distance between two nodes of these protein interaction networks indicates that it is quite short comparing with the large network size. The plot of the logarithm of the frequency vs. the shortest path length also indicates that the shortest path length distribution follows a
Graphlet decomposition of a weighted network
"... We introduce the graphlet decomposition of a weighted network, which encodes a notion of social information based on social structure. We develop a scalable algorithm, which combines EM with BronKerbosch in a novel fashion, for estimating the parameters of the model underlying graphlets using one n ..."
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We introduce the graphlet decomposition of a weighted network, which encodes a notion of social information based on social structure. We develop a scalable algorithm, which combines EM with BronKerbosch in a novel fashion, for estimating the parameters of the model underlying graphlets using one network sample. We explore theoretical properties of graphlets, including computational complexity, redundancy and expected accuracy. We test graphlets on synthetic data, and we analyze messaging on Facebook and crime associations in the 19th century. 1