Efficient Calculation of Triangle Centrality in Big Data Networks

Wali Mohammad Abdullah, David Awosoga, S. Hossain
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引用次数: 1

Abstract

The notion of “centrality” within graph analytics has led to the creation of well-known metrics such as Google's Page Rank [1], which is an extension of eigenvector centrality [2]. Triangle centrality is a related metric [3] that utilizes the presence of triangles, which play an important role in network analysis, to quantitatively determine the relative “importance” of a node in a network. Efficiently counting and enumerating these triangles are a major backbone to understanding network characteristics, and linear algebraic methods have utilized the correspondence between sparse adjacency matrices and graphs to perform such calculations, with sparse matrix-matrix multiplication as the main computational kernel. In this paper, we use an intersection representation of graph data implemented as a sparse matrix, and engineer an algorithm to compute the triangle centrality of each vertex within a graph. The main computational task of calculating these sparse matrix-vector products is carefully crafted by employing compressed vectors as accumulators. As with other state-of-the-art algorithms [4], our method avoids redundant work by counting and enumerating each triangle exactly once. We present results from extensive computational experiments on large-scale real-world and synthetic graph in-stances that demonstrate good scalability of our method. We also present a shared memory parallel implementation of our algorithm.
大数据网络中三角中心性的高效计算
图分析中的“中心性”概念导致了众所周知的指标的创建,如谷歌的页面排名[1],它是特征向量中心性[2]的扩展。三角形中心性是一种相关度量[3],它利用三角形的存在来定量确定网络中节点的相对“重要性”,三角形在网络分析中起着重要作用。有效地计数和枚举这些三角形是理解网络特征的主要支柱,线性代数方法利用稀疏邻接矩阵和图之间的对应关系来执行这种计算,稀疏矩阵-矩阵乘法是主要的计算内核。在本文中,我们使用图形数据的交集表示实现为稀疏矩阵,并设计了一种算法来计算图中每个顶点的三角形中心性。计算这些稀疏矩阵-向量乘积的主要计算任务是通过使用压缩向量作为累加器来精心设计的。与其他最先进的算法[4]一样,我们的方法通过精确计数和枚举每个三角形一次来避免冗余工作。我们在大规模的真实世界和合成图实例上进行了大量的计算实验,结果表明我们的方法具有良好的可扩展性。我们还提出了我们算法的共享内存并行实现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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