Finding all cycles in a directed graph

Question

How can I find (iterate over) ALL the cycles in a directed graph from/to a given node?

For example, I want something like this:

A->B->A
A->B         


        

Answer 1

Depth first search with backtracking should work here. Keep an array of boolean values to keep track of whether you visited a node before. If you run out of new nodes to go to (without hitting a node you have already been), then just backtrack and try a different branch.

The DFS is easy to implement if you have an adjacency list to represent the graph. For example adj[A] = {B,C} indicates that B and C are the children of A.

For example, pseudo-code below. "start" is the node you start from.

dfs(adj,node,visited):  
  if (visited[node]):  
    if (node == start):  
      "found a path"  
    return;  
  visited[node]=YES;  
  for child in adj[node]:  
    dfs(adj,child,visited)
  visited[node]=NO;

Call the above function with the start node:

visited = {}
dfs(adj,start,visited)