2-Edge-Connected Components Example

Graph: $0-1$, $1-2$, $2-0$, $1-3$, $3-4$, $4-3$. Bridges: $\{1-3\}$. Remove it. You get two components: $\{0, 1, 2\}$ and $\{3, 4\}$. Component $\{0, 1, 2\}$ is a $2$-edge-connected cycle. Remove any edge from this triangle, and the component stays connected because there is always an alternate path through the other two edges.

Component $\{3, 4\}$ is another $2$-edge-connected cycle between vertices $3$ and $4$. The bridge $1-3$ connects these two resilient components.