Given a small graph, how can you manually calculate the number of automorphisms? I thought of seeing the number of nodes of a particular degree and permuting among them, but aren't there other factors to consider, like the node being part of a cycle, etc? For example, this graph:
Suppose b had two more edges going to two different nodes, then you can't map b to g, even though they have the same degree. So how do you do this?