On wikipedia the definition of a cycle in a graph is given by : "In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices". I was confused because other websites say: " A cycle is a circuit in which no vertex except the first (which is also the last) appears more than once". The second definition seems to be the most common one so I assume that one to be the proper definition.
Now, on to some more confusing stuff. On "p.42" of the Graph Theory book by Bondy and Murty, they claim that : "Every cycle in a graph is a maximal cycle, because no cycle is contained in another; by the same token, every cycle is a minimal cycle". Is this true though? You could have a double-necklace for example. One of its loops is a loop by definition, but so is the double loop, and the single loop is contained in the double loop. Can anyone shed some light on this?