Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from multiple domains. Counting subgraphs is, however, computationally very expensive, and there has been a large body of work on efficient algorithms and strategies to make subgraph counting feasible for larger subgraphs and networks. This survey aims precisely to provide a comprehensive overview of the existing methods for subgraph counting. Our main contribution is a general and structured review of existing algorithms, classifying them on a set of key characteristics, highlighting their main similarities and differences. We identify and describe the main conceptual approaches, giving insight on their advantages and limitations, and we provide pointers to existing implementations. We initially focus on exact sequential algorithms, but we also do a thorough survey on approximate methodologies (with a trade-off between accuracy and execution time) and parallel strategies (that need to deal with an unbalanced search space).

中文翻译：

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子图计数综述

计算子图频率是一项基本任务，它是几种网络分析方法的核心，例如网络主题和基于图形的度量，它们已被广泛用于对来自多个域的网络进行分类和比较。然而，计算子图在计算上非常昂贵，并且已经有大量关于有效算法和策略的工作，以使子图计数对于更大的子图和网络变得可行。本次调查旨在提供对现有子图计数方法的全面概述。我们的主要贡献是对现有算法的一般性和结构化审查，根据一组关键特征对它们进行分类，突出它们的主要相似之处和不同之处。我们确定并描述了主要的概念方法，深入了解它们的优点和局限性，并提供指向现有实现的指针。我们最初专注于精确的顺序算法，但我们也对近似方法（在准确性和执行时间之间进行权衡）和并行策略（需要处理不平衡的搜索空间）进行了彻底的调查。