Abstract. Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n 2 log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are also the worstcase time bounds for computing the betweenness score of a single vertex. In this paper, we present a novel approximation algorithm for computing betweenness centrality of a given vertex, for both weighted and unweighted graphs. Our approximation algorithm is based on an adaptive sampling technique that significantly reduces the number of single-source shortest path computations for vertices with high centrality. We conduct an extensive experimental study on real-world graph instances, and observe that our random sampling algorithm gives very good betweenness approximations for biological networks, road networks and web crawls.

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.

Data-intensive, graph-based computations are pervasive in several scientific applications, and are known to to be quite challenging to implement on distributed memory systems. In this work, we explore the design space of parallel algorithms for Breadth-First Search (BFS), a key subroutine in several graph algorithms. We present two highly-tuned parallel approaches for BFS on large parallel systems: a levelsynchronous strategy that relies on a simple vertex-based partitioning of the graph, and a two-dimensional sparse matrixpartitioning-based approach that mitigates parallel communication overhead. For both approaches, we also present hybrid versions with intra-node multithreading. Our novel hybrid two-dimensional algorithm reduces communication times by up to a factor of 3.5, relative to a common vertex based approach. Our experimental study identifies execution regimes in which these approaches will be competitive, and we demonstrate extremely high performance on leading distributed-memory parallel systems. For instance, for a 40,000-core parallel execution on Hopper, an AMD MagnyCours based system, we achieve a BFS performance rate of 17.8 billion edge visits per second on an undirected graph of 4.3 billion vertices and 68.7 billion edges with skewed degree distribution.

Abstract

We present SNAP (Small-world