Abstract Strongly connected components (SCCs) are an important kind of subgraphs in digraphs. It can be viewed as a kind of knowledge in the viewpoint of knowledge discovery. In our previous work, a knowledge discovery algorithm called RSCC was proposed for finding SCCs of simple digraphs based on two operators, k-step R-related set and k-step upper approximation, of rough set theory (RST). RSCC algorithm can find SCCs more efficiently than Tarjan algorithm of linear complexity. However, on the one hand, as the theoretical basis of RST applied to SCCs discovery of digraphs, the theoretical relationships between RST and graph theory investigated in previous work only include four equivalences between fundamental RST and graph concepts relating to SCCs. The reasonability of using the two RST operators to find SCCs still need to be investigated. On the other hand, it is found that there are three SCCs correlations between vertices after we use three RST concepts, R-related set, lower and upper approximation sets, to analyze SCCs. RSCC algorithm ignores these SCCs correlations so that the efficiency of RSCC is affected negatively. For the above two issues, firstly, we explore the equivalence between the two RST operators and Breadth-First Search (BFS) which is one of the most basic graph search algorithms and the most direct way to find SCCs. These equivalences explain the reasonability of using the two RST operators to find SCCs, and enrich the content of the theoretical relationships between RST and graph theory. Secondly, we design a granulation strategy according to these three SCCs correlations. Then an algorithm called GRSCC for finding SCCs of simple digraphs based on granulation strategy is proposed. Experimental results show that GRSCC provides better performance to RSCC.

中文翻译：

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基于粒化策略寻找简单有向图的强连通分量

摘要 强连通分量（SCC）是有向图中的一种重要子图。从知识发现的角度来看，它可以看作是一种知识。在我们之前的工作中，提出了一种称为 RSCC 的知识发现算法，用于基于粗糙集理论 (RST) 的 k 步 R 相关集和 k 步上近似两个算子来查找简单有向图的 SCC。RSCC 算法可以比线性复杂度的 Tarjan 算法更有效地找到 SCC。然而，一方面，作为 RST 应用于 SCCs 发现有向图的理论基础，先前工作中研究的 RST 与图论之间的理论关系仅包括基本 RST 与 SCC 相关图概念之间的四个等价。使用两个 RST 算子寻找 SCC 的合理性还有待研究。另一方面，在我们使用三个RST概念，R相关集，下和上近似集来分析SCC后，发现顶点之间存在三个SCC相关性。RSCC 算法会忽略这些 SCC 的相关性，从而对 RSCC 的效率产生负面影响。针对以上两个问题，我们首先探讨了两个 RST 算子与广度优先搜索（BFS）的等价性，BFS 是最基本的图搜索算法之一，也是寻找 SCC 的最直接方式。这些等价解释了使用两个 RST 算子寻找 SCC 的合理性，丰富了 RST 与图论之间的理论关系内容。其次，我们根据这三个 SCC 的相关性设计了制粒策略。然后提出了一种基于粒化策略寻找简单有向图的SCC的算法，称为GRSCC。实验结果表明，GRSCC 为 RSCC 提供了更好的性能。