In the functiondetectUndirectedCycle, the cycle path is being constructed as an object with vertex keys as properties and their parent vertices as values. This makes the returnedcycle not a standard path array, but rather a mapping, which may not be intuitive or useful for consumers expecting an ordered path of vertices forming the cycle. A more conventional approach would be to return anordered array of vertices representing the cycle, starting and ending at the same vertex.
Additionally, if a cycle is detected, the function continues to traverse the graph until DFS completes, although traversal is blocked byallowTraversal once a cycle is set. However, early exit after detecting a cycle could improve efficiency.

Suggested Fix:

• Changecycle to be an array that accumulates the ordered path of the cycle.
• Optionally, add a mechanism to exit the traversal immediately after the cycle is found.