Ulrik Brandes

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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 Θ(n) time and Θ(n) space, where n is the number of actors in the network. Motivated by the fast-growing need to compute centrality indices on large, yet very sparse, networks, new algorithms for betweenness(More)
Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for(More)
We present a novel sampling-based approximation technique for classical multidimensional scaling that yields an extremely fast layout algorithm suitable even for very large graphs. It produces layouts that compare favorably with other methods for drawing large graphs, and it is among the fastest methods available. In addition, our approach allows for(More)
Centrality indices are an essential concept in network analysis. For those based on shortest-path distances the computation is at least quadratic in the number of nodes, since it usually involves solving the single-source shortest-paths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today.(More)
Following a workshop on graph data formats held with the 8th Symposium on Graph Drawing (GD 2000), a task group was formed to propose a format for graphs and graph drawings that meets current and projected requirements. On behalf of this task group, we here present GraphML (Graph Markup Language), an XML format for graph structures, as an initial step(More)
We consider variations of two well-known 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 current-flow variant of closeness centrality is identical with another known measure,(More)
Random networks are frequently generated, for example, to investigate the effects of model parameters on network properties or to test the performance of algorithms. Recent interest in the statistics of large-scale networks sparked a growing demand for network generators that can generate large numbers of large networks quickly. We here present simple and(More)
In this paper we give models and algorithms to describe and analyze the collaboration among authors of Wikipedia from a network analytical perspective. The edit network encodes who interacts how with whom when editing an article; it significantly extends previous network models that code author communities in Wikipedia. Several characteristics summarizing(More)
We propose a two-phase heuristic for crossing reduction in circular layouts. While the first algorithm uses a greedy policy to build a good initial layout, an adaptation of the sifting heuristic for crossing reduction in layered layouts is used for local optimization in the second phase. Both phases are conceptually simpler than previous heuristics, and our(More)