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122
The structure and function of complex networks
 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, ..."
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Cited by 1407 (9 self)
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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, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
A measure of betweenness centrality based on random walks
 Social Networks
, 2005
"... Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the n ..."
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Cited by 139 (0 self)
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Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks. 1
Coauthorship networks and patterns of scientific collaboration
 In Proceedings of the National Academy of Sciences
, 2004
"... Using data from three bibliographic databases in biology, physics, and mathematics respectively, networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper together. We use these networks to answer a broad variety of questions about co ..."
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Cited by 121 (0 self)
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Using data from three bibliographic databases in biology, physics, and mathematics respectively, networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper together. We use these networks to answer a broad variety of questions about collaboration patterns, such as the numbers of papers authors write, how many people they write them with, what the typical distance between scientists is through the network, and how patterns of collaboration vary between subjects and over time. We also summarize a number of recent results by other authors on coauthorship patterns. 1
Clustering and preferential attachment in growing networks
 Phys. Rev. E
, 2001
"... We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of o ..."
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Cited by 102 (6 self)
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We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and powerlaw degree distributions in networks. 1 I.
SmallWorld FileSharing Communities
, 2003
"... Web caches, content distribution networks, peertopeer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can fi ..."
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Cited by 68 (9 self)
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Web caches, content distribution networks, peertopeer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can first identify and then exploit interesting structure within a community's access patterns. To this end, we propose a novel perspective on file sharing based on the study of the relationships that form among users based on the files in which they are interested. We propose a new structure that captures common user interests in datathe datasharing graph and justify its utility with studies on three datadistribution systems: a highenergy physics collaboration, the Web, and the Kazaa peertopeer network. We find smallworld patterns in the datasharing graphs of all three communities. We analyze these graphs and propose some probable causes for these emergent smallworld patterns. The significance of smallworld patterns is twofold: it provides a rigorous support to intuition and, perhaps most importantly, it suggests ways to design mechanisms that exploit these naturally emerging patterns.
Detecting richclub ordering in complex networks,” Arxiv preprint physics/0602134
, 2006
"... Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1, 2, 3, 4, 5]. The “richclub ..."
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Cited by 35 (0 self)
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Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1, 2, 3, 4, 5]. The “richclub” phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences [4, 5, 6]. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the richclub phenomenon. The presented analysis enables the measurement of the richclub ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains 1.
kcore decomposition: a tool for the visualization of large scale networks
"... We use the kcore decomposition to visualize large scale complex networks. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develo ..."
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Cited by 30 (2 self)
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We use the kcore decomposition to visualize large scale complex networks. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develop a general visualization algorithm that can be used to compare the structure of various networks and highlight their hierarchical structure. The low computational complexity of the algorithm O(n), where n is the size of the network, makes it suitable for the visualization of very large networks. We apply the proposed visualization tool to several real and synthetic graphs, showing its utility in finding specific structural fingerprints of computer generated and real world networks.
2005) Studying the Emerging Global Brain: Analyzing and Visualizing the Impact of CoAuthorship Teams
 Complexity, Special issue on Understanding Complex Systems
, 2005
"... This article introduces a suite of approaches and measures to study the impact of coauthorship teams based on the number of publications and their citations on a local and global scale. In particular, we present a novel weighted graph representation that encodes coupled authorpaper networks as a w ..."
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Cited by 29 (3 self)
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This article introduces a suite of approaches and measures to study the impact of coauthorship teams based on the number of publications and their citations on a local and global scale. In particular, we present a novel weighted graph representation that encodes coupled authorpaper networks as a weighted coauthorship graph. This weighted graph representation is applied to a dataset that captures the emergence of a new field of science and comprises 614 articles published by 1036 unique authors between 1974 and 2004. To characterize the properties and evolution of this field, we first use four different measures of centrality to identify the impact of authors. A global statistical analysis is performed to characterize the distribution of paper production and paper citations and its correlation with the coauthorship team size. The size of coauthorship clusters over time is examined. Finally, a novel local, authorcentered measure based on entropy is applied to determine the global evolution of the field and the identification of the contribution of a single author’s impact across all of its coauthorship relations. A visualization of the growth of the weighted coauthor network, and the results obtained from the statistical analysis indicate a drift toward a more cooperative, global collaboration process as the main drive in the production of scientific knowledge.
Bipartite Graphs as Models of Complex Networks
 Aspects of Networking
, 2004
"... It appeared recently that the classical random graph model used to represent realworld complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here the first model which achieves the following challenges: it produces ..."
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Cited by 29 (4 self)
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It appeared recently that the classical random graph model used to represent realworld complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here the first model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some realworld observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution. Indeed, we show that any complex network can be viewed as a bipartite graph with some specific characteristics, and that its main properties can be viewed as consequences of this underlying structure. We also propose a growing model based on this observation. Introduction.
Information Dynamics in the Networked World
 In Lecture Notes in Physics
, 2004
"... Summary. We review three studies of information flow in social networks that help reveal their underlying social structure, how information spreads through them and why small world experiments work. 1 ..."
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Cited by 24 (3 self)
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Summary. We review three studies of information flow in social networks that help reveal their underlying social structure, how information spreads through them and why small world experiments work. 1