Bridge Algorithm Walkthrough

Graph: $0-1$, $1-2$, $0-2$, $1-3$. Start DFS at $0$. Visit $0$: disc[0]=0, low[0]=0. Visit $1$: disc[1]=1, low[1]=1. Visit $2$: disc[2]=2, low[2]=2. Back edge $2-0$: low[2]=min(2,0)=0. Backtrack to $1$: low[1]=min(1,0)=0.

Visit $3$: disc[3]=3, low[3]=3. Backtrack to $1$: check low[3]=3 > disc[1]=1, so edge $1-3$ is a bridge. Final bridges: $\{1-3\}$. All other edges are part of the cycle $0-1-2-0$.