Strongly Connected Components

In a directed graph — arrows, not plain lines, connecting nodes — a strongly connected component (SCC) is a maximal set of nodes where you can get from any node in the set to any other node in the set by following the arrows, in both directions if needed. A single node is trivially its own SCC if it has no cycle through it; a group of nodes all pointing around in a loop (A → B → C → A) forms one SCC of size three.

The standard use case is dependency analysis: if module A imports module B, draw an arrow A → B. Tarjan's or Kosaraju's algorithm finds all SCCs in linear time, and any SCC with more than one node is a circular dependency — a group of modules that can't be built, tested, or reasoned about independently because each ultimately depends on the others.

Worked example. A codebase's import graph has modules pricing, risk, data, utils. If pricing imports risk, risk imports data, and data imports pricing back, those three form one SCC — a cycle that means you cannot understand pricing in isolation from risk or data. Running Tarjan's algorithm on the full import graph flags this three-module cycle instantly, even buried among hundreds of files, letting you refactor to break the loop (typically by extracting the shared piece both sides depend on into its own module) before it causes an unpredictable build order or a subtle circular-import bug.