A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path corresponds to the last.
This is the definition of cycle in the WolframMathWorld page. I don't understand how a cycle becomes a circuit if the 1st vertex is not specified.
I thought :
a circuit is a closed walk with no repeated EDGES.
a cycle is a closed walk with no repeated edges and no repeated vertices