Parallel Algorithms for Evaluating Centrality Indices in Real-world Networks

Abstract

This paper discusses fast parallel algorithms for evaluating several centrality indices frequently used in complex network analysis. These algorithms have been optimized to exploit properties typically observed in real-world large scale networks, such as the low average distance, high local density, and heavy-tailed power law degree distributions. We test our implementations on real datasets such as the web graph, protein-interaction networks, movie-actor and citation networks, and report impressive parallel performance for evaluation of the computationally intensive centrality metrics (betweenness and closeness centrality) on high-end shared memory symmetric multiprocessor and multithreaded architectures. To our knowledge, these are the first parallel implementations of these widely-used social network analysis metrics. We demonstrate that it is possible to rigorously analyze networks three orders of magnitude larger than instances that can be handled by existing network analysis (SNA) software packages. For instance, we compute the exact betweenness centrality value for each vertex in a large US patent citation network (3 million patents, 16 million citations) in 42 minutes on 16 processors, utilizing 20GB RAM of the IBM p5 570. Current SNA packages on the other hand cannot handle graphs with more than hundred thousand edges.

Toward a distance oracle for billion-node graphs

“…• Second, although some parallel approaches for computing exact betweenness have been proposed [17,18,19,20,21], in general, it is still very costly for billion-node graphs. A straightforward parallel compuation of the exact betweenness has complexity Ω(|V | 2 ) [19], which is prohibitive on big graphs.…”

The Power of Quasi-Shortest Paths: $\rho$ -Geodesic Betweenness Centrality

“…The complexity of our metric can be further reduced if the algorithm is parallelized, which is a matter of parallelizing the single-source shortest paths (SSSP) and the accumulation functions in Brandes' algorithm [33], considering unweighted networks. This is feasible [34], [35], [36], [37] and the graph traversal performed in the SSSP needs to be run ρ + 1 times to find all the paths we need to compute the ρ-geodesic betweenness. In addition, if only local knowledge is available, it is possible to modify a distributed algorithm as the one proposed by Lehman and Kaufman [38] to compute our metric.…”

A Java-Based Distributed Approach for Generating Large-Scale Social Network Graphs

“…A very important topic for distributed applications is Big Data management and more specifically the generation of large-scale social networks graphs where the number of nodes reaches very large numbers. Analysis of such networks is of importance in many areas, e.g., data mining, network sciences, physics, and social sciences [3]. The need for efficient and scalable methods of network generation is frequently mentioned in the literature [8], particularly for the preferential attachment process [1,13,14].…”