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 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.

Matching is a popular combinatorial optimization problem with numerous applications in both commercial and scientific fields. Computing optimal matchings w.r.t. cardinality or weight can be done in polynomial time; still, this task can become infeasible for very large networks. Thus, several approximation algorithms that trade solution quality for a faster running time have been proposed. For networks that change over time, fully dynamic algorithms that efficiently maintain an approximation of the optimal matching after a graph update have been introduced as well. However, no semi- or fully dynamic algorithm for (approximate) maximum weighted matching has been implemented. In this article, we focus on the problem of maintaining a \( 1/2 \) -approximation of a maximum weighted matching (MWM) in fully dynamic graphs. Limitations of existing algorithms for this problem are (i) high constant factors in their time complexity, (ii) the fact that none of them supports batch updates, and (iii) the lack of a practical implementation, meaning that their actual performance on real-world graphs has not been investigated. We propose and implement a new batch-dynamic \( 1/2 \) -approximation algorithm for MWM based on the Suitor algorithm and its local edge domination strategy [Manne and Halappanavar, IPDPS 2014]. We provide a detailed analysis of our algorithm and prove its approximation guarantee. Despite having a worst-case running time of \( \mathcal {O}(n + m) \) for a single graph update, our extensive experimental evaluation shows that our algorithm is much faster in practice. For example, compared to a static recomputation with sequential Suitor , single-edge updates are handled up to \( 10^5\times \) to \( 10^6\times \) faster, while batches of \( 10^4 \) edge updates are handled up to \( 10^2\times \) to \( 10^3\times \) faster.

In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group closeness maximization, in turn, is more challenging: the objective is to find a vertex group that is central as a whole and state-of-the-art heuristics for it do not scale to very big graphs yet. In this paper, we present new local search heuristics for group closeness maximization. By using randomized approximation techniques and dynamic data structures, our algorithms are often able to perform locally optimal decisions efficiently. The final result is a group with high (but not optimal) closeness centrality. We compare our algorithms to the current state-of-the-art greedy heuristic both on weighted and on unweighted real-world graphs. For graphs with hundreds of millions of edges, our local search algorithms take only around ten minutes, while greedy requires more than ten hours. Overall, our new algorithms are between one and two orders of magnitude faster, depending on the desired group size and solution quality. For example, on weighted graphs and $k = 10$, our algorithms yield solutions of $12,4\%$ higher quality, while also being $793,6\times$ faster. For unweighted graphs and $k = 10$, we achieve solutions within $99,4\%$ of the state-of-the-art quality while being $127,8\times$ faster.

The ubiquity of massive graph data sets in numerous applications requires fast algorithms for extracting knowledge from these data. We are motivated here by three electrical measures for the analysis of large small-world graphs $G = (V, E)$ -- i.e., graphs with diameter in $O(\log |V|)$, which are abundant in complex network analysis. From a computational point of view, the three measures have in common that their crucial component is the diagonal of the graph Laplacian's pseudoinverse, $L^\dagger$. Computing diag$(L^\dagger)$ exactly by pseudoinversion, however, is as expensive as dense matrix multiplication -- and the standard tools in practice even require cubic time. Moreover, the pseudoinverse requires quadratic space -- hardly feasible for large graphs. Resorting to approximation by, e.g., using the Johnson-Lindenstrauss transform, requires the solution of $O(\log |V| / \epsilon^2)$ Laplacian linear systems to guarantee a relative error, which is still very expensive for large inputs. In this paper, we present a novel approximation algorithm that requires the solution of only one Laplacian linear system. The remaining parts are purely combinatorial -- mainly sampling uniform spanning trees, which we relate to diag$(L^\dagger)$ via effective resistances. For small-world networks, our algorithm obtains a $\pm \epsilon$-approximation with high probability, in a time that is nearly-linear in $|E|$ and quadratic in $1 / \epsilon$. Another positive aspect of our algorithm is its parallel nature due to independent sampling. We thus provide two parallel implementations of our algorithm: one using OpenMP, one MPI + OpenMP. In our experiments against the state of the art, our algorithm (i) yields more accurate results, (ii) is much faster and more memory-efficient, and (iii) obtains good parallel speedups, in particular in the distributed setting.