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74
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 of the same cluster and comparatively few edges joining vertices of different clusters. Such
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. ..."
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Cited by 540 (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.
Contraction hierarchies: Faster and simpler . . .
, 2008
"... We present a route planning technique solely based on the concept of node contraction. We contract or remove one node at a time out of the graph and add shortcut edges to the remaining graph to preserve shortest paths distances. The resulting contraction hierarchy (CH), the original graph plus short ..."
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Cited by 116 (32 self)
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We present a route planning technique solely based on the concept of node contraction. We contract or remove one node at a time out of the graph and add shortcut edges to the remaining graph to preserve shortest paths distances. The resulting contraction hierarchy (CH), the original graph plus shortcuts, also defines an order of “importance ” among all nodes through the node selection. We apply a modified bidirectional Dĳkstra algorithm that takes advantage of this node order to obtain shortest paths. The search space is reduced by relaxing only edges leading to more important nodes in the forward search and edges coming from more important nodes in the backward search. Both search scopes eventually meet at the most important node on a shortest path. We use a simple but extensible heuristic to obtain the node order: a priority queue whose priority function for each node is a linear combination of several terms, e.g. one term weights nodes depending on the sparsity of the remaining graph after the contraction. Another term regards the already contracted nodes to allow a more uniform contraction. Depending on the application we can select the combination of the priority terms to obtain the required hierarchy.
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 83 (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.
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 75 (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 54 (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.
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 53 (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
 IEEE Transactions on Visualization and Computer Graphics
, 2003
"... ..."
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 41 (4 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.