Introduction In graph theory, particularly in the context of directed graphs, identifying groups of nodes that form closed loops is a foundational task. These groups, known as strongly connected components (SCCs) , are essential in areas such as compiler optimization, social network analysis, and distributed systems. A strongly connected component is a maximal subgraph in which every pair of nodes is reachable from one another. Detecting SCCs efficiently becomes crucial when analyzing large-scale graphs. Tarjan’s Algorithm , developed by Robert Tarjan in 1972, is a classic and highly efficient method for finding SCCs using a single pass of depth-first search (DFS). It is both time- and space-efficient and remains widely used in modern graph processing systems.