I am given a graph defined by vertexes and edges. I have to obtain all the cycle bases in a network. **No coordinates will be given for the nodes.**


Here's a [sketch](http://deluxecourse.com/network.png) that illustrates my point.


**Note that inside a cycle it must not contain any edge**



Algorithm to find all the cycle bases in a graph
Maybe what you want is a cycle basis? That is, a set of cycles such that any other cycle can be found by adding and subtracting combinations of cycles in the basis. One can find a cycle basis easily for any graph by finding a spanning tree and then, for each edge that's not in the tree, reporting the cycle formed by that edge together with the tree path connecting its endpoints. In a plane-embedded graph, the set of interior faces forms a cycle basis, matching what the sketch describes. Finding the shortest cycle basis is more complicated but still known in polynomial time; see e.g. [Kavitha et al, ICALP 2004](http://dx.doi.org/10.1007/b99859).


