Cycle detection techniques can be different when it comes to directed and undirected graphs. Understanding these differences is important for using the right method.

Key Differences:

1. Graph Structure:

   • Directed Graphs: Here, edges point in one direction. This creates one-way connections. Because of this, cycles, or loops, can form in special ways.
   • Undirected Graphs: In these graphs, edges connect both ways. So, a cycle must connect through mutual links.

2. Algorithms Used:

   • Directed Graphs: We can use a method called Depth-First Search (DFS). This uses a color system (white, gray, black) to track nodes. If a node goes back to being gray (open), it means we've found a cycle.
   • Undirected Graphs: We can use either DFS or Breadth-First Search (BFS). A key part is checking for back edges. If we find a visited node that isn't the direct parent of the current node, it means a cycle exists.

Example:

• In a directed graph with points A, B, and C, if the connections are A → B, B → C, and C → A, then a cycle (A, B, C) is present.
• In an undirected graph with points A, B, and C, if the connections are A—B, B—C, and C—A, we can find the same cycle. However, it's easier to see in undirected graphs because the edges don't point in just one direction.