Path P₁, P₂ between vertices u, v.

First graph is biconnected (P₁ ∩ P₂ = {u, v}), second graph is connected with articulation and without bridge (P₁ ∩ P₂ = {u, v, x}) and third graph is connected with bridge (P₁ ∩ P₂ = {u, v, x, (x, v)}).