The field of network science is a highly interdisciplinary area; for the empirical analysis of network data, it draws algorithmic methodologies from several research fields. Hence, research procedures and descriptions of the technical results often differ, sometimes widely. In this paper we focus on methodologies for the experimental part of algorithm engineering for network analysis—an important ingredient for a research area with empirical focus. More precisely, we unify and adapt existing recommendations from different fields and propose universal guidelines—including statistical analyses—for the systematic evaluation of network analysis algorithms. This way, the behavior of newly proposed algorithms can be properly assessed and comparisons to existing solutions become meaningful. Moreover, as the main technical contribution, we provide SimexPal, a highly automated tool to perform and analyze experiments following our guidelines. To illustrate the merits of SimexPal and our guidelines, we apply them in a case study: we design, perform, visualize and evaluate experiments of a recent algorithm for approximating betweenness centrality, an important problem in network analysis. In summary, both our guidelines and SimexPal shall modernize and complement previous efforts in experimental algorithmics; they are not only useful for network analysis, but also in related contexts.

The abundance of massive network data in a plethora of applications makes scalable analysis algorithms and software tools necessary to generate knowledge from such data in reasonable time. Addressing scalability as well as other requirements such as good usability and a rich feature set, the open-source software NetworKit has established itself as a popular tool for large-scale network analysis. This chapter provides a brief overview of the contributions to NetworKit made by the SPP 1736. Algorithmic contributions in the areas of centrality computations, community detection, and sparsification are in the focus, but we also mention several other aspects – such as current software engineering principles of the project and ways to visualize network data within a NetworKit-based workflow.

Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. In this article, we consider the problem of computing rankings for Katz centrality. In particular, we propose upper and lower bounds on the Katz score of a given node. Previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings; however, we construct an algorithm that iteratively improves those upper and lower bounds until a correct Katz ranking is obtained. We extend our algorithm to dynamic graphs while maintaining its correctness guarantees. Experiments demonstrate that our static graph algorithm outperforms both numerical approaches and heuristics with speedups between \( 1.5\times \) and \( 3.5\times \) , depending on the desired quality guarantees. Our dynamic graph algorithm improves upon the static algorithm for update batches of less than 10,000 edges. We provide efficient parallel CPU and GPU implementations of our algorithms that enable near real-time Katz centrality computation for graphs with hundreds of millions of edges in fractions of seconds.

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.

The abundance of massive network data in a plethora of applications makes scalable analysis algorithms and software tools necessary to generate knowledge from such data in reasonable time. Addressing scalability as well as other requirements such as good usability and a rich feature set, the open-source software NetworKit has established itself as a popular tool for large-scale network analysis. This chapter provides a brief overview of the contributions to NetworKit made by the DFG Priority Programme SPP 1736 Algorithms for Big Data. Algorithmic contributions in the areas of centrality computations, community detection, and sparsification are in the focus, but we also mention several other aspects -- such as current software engineering principles of the project and ways to visualize network data within a NetworKit-based workflow.