Nowadays a large amount of data is originated by complex systems, such as social networks, transportation systems, computer and service networks. These systems can be modeled by using graphs and studied by exploiting graph metrics, such as betweenness centrality (BC), a popular metric to analyze node centrality of graphs. In spite of its great potential, this metric requires long computation time, especially for large graphs. In this paper, we present a very fast algorithm to compute BC of undirected graphs by exploiting clustering. The algorithm leverages structural properties of graphs to find classes of equivalent nodes: by selecting one representative node for each class, we are able to compute BC by significantly reducing the number of single-source shortest path explorations adopted by Brandes’ algorithm. We formally prove the graph properties that we exploit to define the algorithm and present an implementation based on Scala for both sequential and parallel map-reduce executions. The experimental evaluation of both versions, conducted with synthetic and real graphs, reveals that our solution largely outperforms Brandes’ algorithm and significantly improves known heuristics.

如今，大量数据源自复杂的系统，例如社交网络、交通系统、计算机和服务网络。这些系统可以通过使用图来建模，并通过利用图度量来研究，例如介数中心性 (BC)，这是一种分析图节点中心性的流行度量。尽管其潜力巨大，但该指标需要很长的计算时间，尤其是对于大型图。在本文中，我们提出了一种非常快速的算法，通过利用聚类来计算无向图的 BC。该算法利用图的结构特性来查找等效节点的类别：通过为每个类别选择一个代表性节点，我们能够通过显着减少 Brandes 算法采用的单源最短路径探索的数量来计算 BC。我们正式证明了我们用来定义算法的图属性，并提出了一个基于 Scala 的实现，用于顺序和并行 map-reduce 执行。使用合成图和真实图对两个版本进行的实验评估表明，我们的解决方案在很大程度上优于 Brandes 的算法，并显着改进了已知的启发式算法。