@inproceedings{Brandes:2002:VBN:509740.509765, abstract = {We describe a novel approach to visualize bibliographic networks that facilitates the simultaneous identification of clusters (e.g., topic areas) and prominent entities (e.g., surveys or landmark papers). While employing the landscape metaphor proposed in several earlier works, we introduce new means to determine relevant parameters of the landscape. Moreover, we are able to compute prominent entities, clustering of entities, and the landscape's surface in a surprisingly simple and uniform way. The effectiveness of our network visualizations is illustrated on data from the graph drawing literature.}, acmid = {509765}, address = {Aire-la-Ville, Switzerland, Switzerland}, author = {Brandes, U. and Willhalm, T.}, booktitle = {Proceedings of the symposium on Data Visualisation 2002}, interhash = {7d070baa654fc70cb8a0b1e373d90e2a}, intrahash = {e5e72eed2d871523dc1100f060658a1c}, isbn = {1-58113-536-X}, location = {Barcelona, Spain}, pages = {159--ff}, publisher = {Eurographics Association}, series = {VISSYM '02}, title = {Visualization of bibliographic networks with a reshaped landscape metaphor}, url = {http://portal.acm.org/citation.cfm?id=509740.509765}, year = 2002 } @article{brandes2001faster, abstract = {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.}, author = {Brandes, U.}, id = {297939}, interhash = {dff547c1a86412c8f3742aab68f7a243}, intrahash = {89019a800a0250d69afda3d11be16196}, journal = {Journal of Mathematical Sociology}, number = 2, pages = {163--177}, priority = {2}, title = {A faster algorithm for betweenness centrality}, url = {http://citeseer.ist.psu.edu/brandes01faster.html}, volume = 25, year = 2001 } @article{brandes2003experiments, author = {Brandes, U. and Gaertler, M. and Wagner, D.}, interhash = {b527c5ab05bac6d10b7768c08fdf7860}, intrahash = {191613112620e6261271504e5cf992e1}, journal = {Lecture notes in computer science}, pages = {568--579}, publisher = {Springer}, title = {{Experiments on graph clustering algorithms}}, url = {http://scholar.google.de/scholar.bib?q=info:gDNQfOoSm6cJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=2}, year = 2003 } @misc{Brandes2006, abstract = {Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.}, author = {Brandes, U. and Delling, D. and Gaertler, M. and Goerke, R. and Hoefer, M. and Nikoloski, Z. and Wagner, D.}, interhash = {3e2bf460cff3138de1e855a7cf5d659d}, intrahash = {b5185cbb85b90294fa15dd2e8ea53f5e}, note = {cite arxiv:physics/0608255 Comment: 10 pages, 1 figure}, title = {Maximizing Modularity is hard}, url = {http://arxiv.org/abs/physics/0608255}, year = 2006 } @article{brandes2008modularity, abstract = {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 past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.}, author = {Brandes, U. and Delling, D. and Gaertler, M. and Gorke, R. and Hoefer, M. and Nikoloski, Z. and Wagner, D.}, doi = {10.1109/TKDE.2007.190689}, interhash = {b7195d25a851617a48d4f15bef5ad789}, intrahash = {9e2e5f9d06d2f83be98083175560c835}, issn = {1041-4347}, journal = {Knowledge and Data Engineering, IEEE Transactions on}, month = {feb. }, number = 2, pages = {172 -188}, title = {On Modularity Clustering}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4358966&tag=1}, volume = 20, year = 2008 }