Symmetry factor of Feynman diagrams

Symmetry factors are often confusing, and existing calculation techniques seem to involve excessive drawings and computations. My personal technique is simple:

1. Label both ends of each line with a number .
2. Count the number of labelings that give an equivalent diagram, where equivalent means they can be deformed into each other.

For example, this diagram has , since we can interchange and at the same time, and get the same diagram (assuming the endpoints are fixed).

This one has , coming from

• 
• 
• and at the same time

With a bit of practice, it becomes quite easy to mentally visualize this labeling and quickly get the factor. It doesn’t involve “taking apart” the diagram, or considering the interchange of both vertices and lines separately.

I am actually not sure how to prove this is correct, but it seems to always work.