Why it matters

BCC decomposition analyzes graph robustness. Understanding shapes reliability.

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The architecture

DFS with edge stack.

On articulation: pop until parent edge.

Biconnected componentsDFSedge stackArticulation foundcut vertexPop stackto parent edgeBCCs form tree structure (block-cut tree) useful for further analysis
BCC.
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How it works end to end

Edge stack on DFS.

Pop when articulation identified.

Each pop segment = BCC.

Block-cut tree: BCCs as nodes.