My name is Pablo Fleurquin. I  am a student of M.Sc in Physics at the UIB (Palma de Mallorca, Spain) and I'm also working in the IFISC institute (Institute for Interdisciplinary Science and Complex Systems).

I have a question regarding  the Depth First Search algorithm. I have been looking at the Boost library page but I'm a newbie with this stuff.

Having a directed graph G (that could be a connected graph or not), I want my program to find the cycles within the graph and remove all the edges that are part of them. It doesn't matter which cycle is erased first as long as the result is the graph G without edge that formely were part of a cycle (in other words, the remaining edges are those that doesn´t form cycles) [attached is  example1]

Intuitively, I am sure that using the depth_first_search() function and recalling it recursively for each "new" graph G "with less" cycles will finally arrive to graph G with no cycles.
The problem is that I have the idea, but my knowledge of c++ is not so vast to implement this code.

I would be gratefully, if you could show me a code for this implementation or a function that does that.

Thank you.
Pablo Fleurquin

P.S: Example 2 is a situation that might happen. If the code can be implemented to eliminate these 2 cycles that share a link it would be greate, if not it will work fine as well.