一种有效的有色三胞体普查计数方法
An efficient counting method for the colored triad census
摘要：
三元组普查是理解网络科学中局部结构的一种重要方法，它提供了对网络中三元组行为者之间观察到的关系配置的全面评估。然而，研究人员往往感兴趣的关系和分类节点属性的组合。在这种情况下，需要考虑三元组普查中节点的标签或颜色。在本文中，我们描述了一个有效的算法，用于构建彩色三位一体人口普查，部分基于现有的方法为经典的三位一体人口普查。我们使用经验和模拟数据的无向和有向图的算法的性能进行评估。仿真结果表明，该算法减少了计算时间的许多倍的天真的方法。我们还将彩色三位一体人口普查应用于Zachary空手道俱乐部网络数据集。我们同时显示的算法的效率，和一种方法来进行统计测试的人口普查，形成一个空分布从1,000实现的混合矩阵条件图和比较观察到的有色三重计数的预期。从这一点上，我们证明了该方法的效用，在我们的讨论结果的同质性，异质性，和桥接，同时获得通过有色三重普查。总而言之，所提出的算法为有色三重普查带来了新的实用程序，社会网络分析在一个有效的包。
英文摘要：
The triad census is an important approach to understand local structure in network science, providing comprehensive assessments of the observed relational configurations between triples of actors in a network. However, researchers are often interested in combinations of relational and categorical nodal attributes. In this case, it is desirable to account for the label, or color, of the nodes in the triad census. In this paper, we describe an efficient algorithm for constructing the colored triad census, based, in part, on existing methods for the classic triad census. We evaluate the performance of the algorithm using empirical and simulated data for both undirected and directed graphs. The results of the simulation demonstrate that the proposed algorithm reduces computational time many-fold over the naive approach. We also apply the colored triad census to the Zachary karate club network dataset. We simultaneously show the efficiency of the algorithm, and a way to conduct a statistical test on the census by forming a null distribution from 1,000 realizations of a mixing-matrix conditioned graph and comparing the observed colored triad counts to the expected. From this, we demonstrate the method's utility in our discussion of results about homophily, heterophily, and bridging, simultaneously gained via the colored triad census. In sum, the proposed algorithm for the colored triad census brings novel utility to social network analysis in an efficient package.
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