# Why do source and sink have to be distinct in Ford-Fulkerson?

Recently I have been studying the Ford-Fulkerson algorithm for determining max flow. I do not see why it is not allowed to have the source vertex be the same as the sink vertex. From what I have heard, doing this allows infinite flow. However if you take a graph where the source (which equals the sink) has no arcs leading into it shouldn't the max flow be $0$?

In the Maximum Flow problem at first step you assume that source has $\infty$ capacity, if it had limited capacity you would denote that by auxiliary arc to node.
Otherwise if source had $0$ capacity then there would be no flow at all.