/// <summary>
        /// Adds temporary edges to the graph to make all vertex even.
        /// </summary>
        /// <param name="g"></param>
        /// <returns></returns>
        public EdgeCollection AddTemporaryEdges(IMutableVertexAndEdgeListGraph g)
        {
            if (g == null)
            {
                throw new ArgumentNullException("g");
            }

            // first gather odd edges.
            VertexCollection oddVertices = AlgoUtility.OddVertices(g);

            // check that there are an even number of them
            if (oddVertices.Count % 2 != 0)
            {
                throw new Exception("number of odd vertices in not even!");
            }

            // add temporary edges to create even edges:
            EdgeCollection ec = new EdgeCollection();

            bool found, foundbe, foundadjacent;

            while (oddVertices.Count > 0)
            {
                IVertex u = oddVertices[0];
                // find adjacent odd vertex.
                found         = false;
                foundadjacent = false;
                foreach (IEdge e in g.OutEdges(u))
                {
                    IVertex v = e.Target;
                    if (v != u && oddVertices.Contains(v))
                    {
                        foundadjacent = true;
                        // check that v does not have an out-edge towards u
                        foundbe = false;
                        foreach (IEdge be in g.OutEdges(v))
                        {
                            if (be.Target == u)
                            {
                                foundbe = true;
                                break;
                            }
                        }
                        if (foundbe)
                        {
                            continue;
                        }
                        // add temporary edge
                        IEdge tempEdge = g.AddEdge(v, u);
                        // add to collection
                        ec.Add(tempEdge);
                        // remove u,v from oddVertices
                        oddVertices.Remove(u);
                        oddVertices.Remove(v);
                        // set u to null
                        found = true;
                        break;
                    }
                }

                if (!foundadjacent)
                {
                    // pick another vertex
                    if (oddVertices.Count < 2)
                    {
                        throw new Exception("Eulerian trail failure");
                    }
                    IVertex v        = oddVertices[1];
                    IEdge   tempEdge = g.AddEdge(u, v);
                    // add to collection
                    ec.Add(tempEdge);
                    // remove u,v from oddVertices
                    oddVertices.Remove(u);
                    oddVertices.Remove(v);
                    // set u to null
                    found = true;
                }

                if (!found)
                {
                    oddVertices.Remove(u);
                    oddVertices.Add(u);
                }
            }

            temporaryEdges = ec;

            return(ec);
        }