Quality functions in community detection

Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated in terms of the optimization of a function, the Newman-Girvan modularity, that is supposed to express the quality of the partitions of a network into communities. Starting from a recent critical survey on modularity optimization, pointing out the existence of a resolution limit that poses severe limits to its applicability, we discuss the general issue of the use of quality functions in community detection. Our main conclusion is that quality functions are useful to compare partitions with the same number of modules, whereas the comparison of partitions with different numbers of modules is not straightforward and may lead to ambiguities.Comment: 10 pages, 4 figures, invited paper to appear in the Proceedings of SPIE International Conference "Fluctuations and Noise 2007", Florence, Italy, 20-24 May, 200

Trigger strategies for SUSY searches at the LHC

Supersymmetry will be searched for in a variety of final states at the LHC. It is crucial that a robust, efficient and unbiased trigger selection for SUSY is implemented from the very early days of data taking. After a brief description of the ATLAS and the CMS trigger systems, and a more in-depth discussion of the ATLAS High-Level Trigger, a triggering strategy is outlined for early SUSY searches at the LHC.Comment: Submitted for the SUSY07 Proceedings, 4 pages, 3 eps figures, LaTe

Community detection algorithms: a comparative analysis

Uncovering the community structure exhibited by real networks is a crucial step towards an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom, Blondel et al. and Ronhovde and Nussinov, respectively, have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.Comment: 12 pages, 8 figures. The software to compute the values of our general normalized mutual information is available at http://santo.fortunato.googlepages.com/inthepress