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.
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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.
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