Working with the list of edges of an undirected graph G
Read the edges of G and create an adjacency matrix A, and simultaneously calculate the degree of each vertex in the array B  # O(m)
- Consider an edge UW, if the data about it already exists A[U][W] == A[W][U] == 1, then a multiple edge is found, skip it
Initialize the queue Q
Add to Q all vertexes whose degree is 2  # O(n) iterations, O(1) get the vertex degree via the array B
- The presence of a vertex in the queue is noted in the array C, which consists of bool flags
Loop until the queue Q is empty:  # O(n) iterations
- Extract vertex V from Q  # V has degree 2 => V located between vertexes U and W
- Delete the edge UV, B[U] -= 1
- Delete the edge VW, B[W] -= 1
- Delete vertex V, C[V] = False
- If U and W are not adjacent, connect U and W with an edge and increase the degrees of U and W by 1  # Checking the adjacency O(1) via the adjacency matrix
- If U's degree is 2 and U is not in queue Q, add U to Q  # Getting vertex degree via B O(1), checking for presence in the queue via C O(1)
- If W's degree is 2 and W is not in queue Q, add W to Q

--Bkarpov96 (talk) 08:17, 7 July 2020 (UTC)