What are some examples of graph cycles?

What are some examples of graph cycles?

Graph cycles are paths that start and end at the same vertex without repeating any edges. A simple example is a triangle formed by three vertices connected in a loop.

Can you give me a more complex example?

Sure! Consider a square with vertices A, B, C, and D. If you connect A to B, B to C, C to D, and D back to A, you create a cycle. You can also have cycles in more complex graphs, like a pentagon or hexagon.

What about cycles in directed graphs?

In directed graphs, cycles can occur when you can follow the directed edges and return to the starting vertex. For example, if you have vertices A, B, and C with edges A -> B, B -> C, and C -> A, that forms a directed cycle.

How do cycles affect graph algorithms?

Cycles can significantly impact graph algorithms, especially in pathfinding and traversal. For instance, algorithms like Dijkstra's may need to handle cycles to avoid infinite loops.