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40
A Faster Algorithm for Betweenness Centrality
 Journal of Mathematical Sociology
, 2001
"... The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require #(n ) time and #(n ) space, where n is the number of actors in the network. ..."
Abstract

Cited by 295 (5 self)
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The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require #(n ) time and #(n ) space, where n is the number of actors in the network.
Visual Unrolling of Network Evolution and the Analysis of Dynamic Discourse
, 2002
"... A new method for visualizing the class of incrementally evolving networks is presented. In addition to the intermediate states of the network it conveys the nature of the change between them by unrolling the dynamics of the network. Each modification is shown in a separate layer of a threedimension ..."
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Cited by 53 (7 self)
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A new method for visualizing the class of incrementally evolving networks is presented. In addition to the intermediate states of the network it conveys the nature of the change between them by unrolling the dynamics of the network. Each modification is shown in a separate layer of a threedimensional representation, where the stack of layers corresponds to a time line of the evolution. We focus on discourse networks as the driving application, but our method extends to any type of network evolving in similar ways.
Applying Social Network Analysis to the Information in CVS Repositories
"... The huge quantities of data available in the CVS repositories of large, longlived libre (free, open source) software projects, and the many interrelationships among those data offer opportunities for extracting large amounts of valuable information about their structure, evolution and internal proc ..."
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Cited by 36 (0 self)
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The huge quantities of data available in the CVS repositories of large, longlived libre (free, open source) software projects, and the many interrelationships among those data offer opportunities for extracting large amounts of valuable information about their structure, evolution and internal processes. Unfortunately, the sheer volume of that information renders it almost unusable without applying methodologies which highlight the relevant information for a given aspect of the project. In this paper, we propose the use of a well known set of methodologies (social network analysis) for characterizing libre software projects, their evolution over time and their internal structure. In addition, we show how we have applied such methodologies to real cases, and extract some preliminary conclusions from that experience.
Communicating Centrality in Policy Network Drawings
, 2003
"... We introduce a network visualization technique that supports an analytical method applied in the social sciences. Policy network analysis is an approach to study policy making structures, processes, and outcomes, thereby concentrating on relations between policy actors. An important operational co ..."
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Cited by 34 (11 self)
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We introduce a network visualization technique that supports an analytical method applied in the social sciences. Policy network analysis is an approach to study policy making structures, processes, and outcomes, thereby concentrating on relations between policy actors. An important operational concept for the analysis of policy networks is the notion of centrality, i.e., the distinction of actors according to their importance in a relational structure. We integrate this measure in a layout model for networks by mapping structural to geometric centrality. Thus, centrality values and network data can be presented simultaneously and explored interactively.
On Variants of ShortestPath Betweenness Centrality and their Generic Computation
 SOCIAL NETWORKS
, 2008
"... Betweenness centrality based on shortest paths is a standard measure of control utilized in numerous studies and implemented in all relevant software tools for network analysis. In this paper, a number of variants are reviewed, placed into context, and shown to be computable with simple variants of ..."
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Cited by 34 (1 self)
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Betweenness centrality based on shortest paths is a standard measure of control utilized in numerous studies and implemented in all relevant software tools for network analysis. In this paper, a number of variants are reviewed, placed into context, and shown to be computable with simple variants of the algorithm commonly used for the standard case. Key words: Betweenness centrality, algorithms, valued networks, load centrality 1
Centrality estimation in large networks
 INTL. JOURNAL OF BIFURCATION AND CHAOS, SPECIAL ISSUE ON COMPLEX NETWORKS’ STRUCTURE AND DYNAMICS
, 2007
"... Centrality indices are an essential concept in network analysis. For those based on shortestpath distances the computation is at least quadratic in the number of nodes, since it usually involves solving the singlesource shortestpaths (SSSP) problem from every node. Therefore, exact computation is ..."
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Cited by 28 (0 self)
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Centrality indices are an essential concept in network analysis. For those based on shortestpath distances the computation is at least quadratic in the number of nodes, since it usually involves solving the singlesource shortestpaths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.
Approximating Betweenness Centrality
, 2007
"... Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationallyexpensive to exactly determine betweenness; currently the fastestknown algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n 2 log n) time for weighted ..."
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Cited by 25 (5 self)
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Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationallyexpensive to exactly determine betweenness; currently the fastestknown algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n 2 log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are also the worstcase time bounds for computing the betweenness score of a single vertex. In this paper, we present a novel approximation algorithm for computing betweenness centrality of a given vertex, for both weighted and unweighted graphs. Our approximation algorithm is based on an adaptive sampling technique that significantly reduces the number of singlesource shortest path computations for vertices with high centrality. We conduct an extensive experimental study on realworld graph instances, and observe that our random sampling algorithm gives very good betweenness approximations for biological networks, road networks and web crawls.
Mixing patterns and community structure in networks
 in Statistical Mechanics of Complex Networks
"... Common experience suggests that many networks might possess community structure—division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of realw ..."
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Cited by 21 (1 self)
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Common experience suggests that many networks might possess community structure—division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of realworld networks and show that they do indeed possess nontrivial community structure. We suggest a possible explanation for this structure in the mechanism of assortative mixing, which is the preferential association of network vertices with others that are like them in some way. We show by simulation that this mechanism can indeed account for community structure. We also look in detail at one particular example of assortative mixing, namely mixing by vertex degree, in which vertices with similar degree prefer to be connected to one another. We propose a measure for mixing of this type which we apply to a variety of networks, and also discuss the implications for network structure and the formation of a giant component in assortatively mixed networks. 1
Centrality Measures Based on Current Flow
, 2005
"... We consider variations of two wellknown centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the currentflow variant of close ..."
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Cited by 20 (2 self)
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We consider variations of two wellknown centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the currentflow variant of closeness centrality is identical with another known measure, information centrality, and give improved algorithms for computing both measures exactly. Since running times and space requirements are prohibitive for large networks, we also present a randomized approximation scheme for currentflow betweenness.