I have a question regarding a graph traversal problem. This is the graph I am working with:
Graph[{1 <-> 2, 1 <-> 3, 2 <-> 3, 2 <-> 4, 3 <-> 4}]
My Problem is following:
I want to find a cycle on this graph such that after completion of the cycle I will have traversed each edge of the graph exactly twice and will have ended at my starting point.
I saw that Mathematica 9 has a built-in function: FindEulerianCycle[g] which does just want I want except that each edge is traversed exactly once. So my idea was to "double" the edges i.e. add a new edge between 2 nodes:
Graph[{
1 <-> 2, 1 <-> 2, 1 <-> 3, 1 <-> 3, 2 <-> 3, 2 <-> 3, 2 <-> 4, 2 <-> 4, 3 <-> 4, 3 <-> 4
}]
But then I get the following error message:
Graph::supp: Mixed graphs and multigraphs are not supported.
Apparently Multigraphs are still not supported in Mathematica 8 & 9: Multigraphs in Mathematica 8
Is there a way to implement a solution to the above mentioned problem in Mathematica? (I am using Mathematica 9)
Note: The graph shown above is just a simple example. I need to solve the above mentioned problem on a much bigger undirected graph which has vertices of odd degree.