Abstract
Network science methodology is increasingly applied to a large variety of real-world phenomena, often leading to big network data sets. Thus, networks (or graphs) with millions or billions of edges are more and more common. To process and analyze these data, we need appropriate graph processing systems and fast algorithms. Yet, many analysis algorithms were pioneered on small networks when speed was not the highest concern. Developing an analysis toolkit for large-scale networks thus often requires faster variants, both from an algorithmic and an implementation perspective. In this paper we focus on computational aspects of vertex centrality measures. Such measures indicate the (relative) importance of a vertex based on the position of the vertex in the network. We describe several common (and some recent and thus less established) measures, optimization problems in their context as well as algorithms for an efficient solution of the raised problems. Our focus is on (not necessarily exact) performance-oriented algorithmic techniques that enable significantly faster processing than the previous state of the art – often allowing to process massive data sets quickly and without resorting to distributed graph processing systems.
Funding statement: This work is partially supported by German Research Foundation (DFG) grant ME 3619/3-2 within Priority Programme 1736 Algorithms for Big Data and by DFG grant ME 3619/4-1.
About the authors
Alexander van der Grinten is a postdoctoral researcher at Humboldt-Universität zu Berlin since August 2018. He received his Ph. D. in Computer Science from University of Cologne, Germany, in January 2018 and his Master degree in Mathematics in 2014. Alexander’s primary research interests include the design and engineering of parallel algorithms in shared-memory and on distributed high-performance systems. He is specifically interested in graph algorithms and the analysis of massive networks, as well as algorithms for hard combinatorial real-world problems.
Eugenio Angriman is a Ph. D. Student at Humboldt-Universität zu Berlin since June 2017. Prior to that he received his Master’s degree in Computer Engineering from Università degli Studi di Padova. Eugenio’s main research interests are scalable algorithms for large-scale network analysis, in particular top-k centrality ranking and group centrality maximization.
Henning Meyerhenke is Full Professor of Computer Science at Humboldt-Universität zu Berlin since August 2018. Prior to that, he was Full Professor at University of Cologne and Assistant Professor at Karlsruhe Institute of Technology. Henning held postdoctoral positions at Georgia Institute of Technology (Atlanta, USA), NEC Laboratories Europe, and University of Paderborn. He received his Diplom degree in Computer Science from Friedrich-Schiller-University Jena in 2004 and his Ph. D. (with highest distinction) in Computer Science from the University of Paderborn in 2008. Henning’s main research interests concern scalable algorithms for large and complex networked systems, in particular for three application areas: algorithmic analysis of large complex networks, combinatorial scientific computing, and applied optimization for algorithmic problems in the natural sciences.
Acknowledgment
We thank the anonymous reviewers of this manuscript for their helpful comments, the co-authors of our works discussed in this overview paper, and all contributors to NetworKit (for the latter, see https://networkit.github.io/credits.html).
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