Algorithms Analysis Practice Test 2025 - Free Algorithms Practice Questions and Study Guide

A graph is said to have cycles if one can traverse edges and revisit the same vertex. This definition highlights that a cycle is formed when there exists a sequence of edges that leads back to the starting vertex without breaking the path rule of traversing edges continuously. In simpler terms, if you can start at a vertex, follow a path along the edges, and return to the same vertex, it confirms the presence of a cycle.

In this context, the type of edges (directed or undirected) does not inherently determine if a cycle exists; rather, it's the act of revisiting a vertex through any connected edges that forms a cycle. This concept applies to both directed and undirected graphs.

The other options don't effectively describe the condition for cycles. For example, while undirected edges may not prevent the formation of cycles, they do not guarantee it either. Having directed edges can also occur in graphs with or without cycles, depending entirely on their arrangement. Lastly, connected components refer to the structure of the graph rather than the presence of cycles, as a graph can have cycles irrespective of its connectivity. Thus, the ability to revisit a vertex during traversal is the crucial criterion for identifying cycles in a graph.