A sequence of vertices v_{1}, v_{2}, \ldots, v_{k} in a graph, where v_{i}=v_{j} only if i=j and k can be any positive integer, is called a cycle if v_{1} is attached by an edge to v_{2}, v_{2} to v_{3}, and so on to v_{k} connected to v_{1}. Rotations and reflections are distinct: A, B, C is distinct from A, C, B and B, C, A. Suppose a simple graph G has 2013 vertices and 3013 edges. What is the minimal number of cycles possible in G?