Simple graph canonization algorithm

I'm looking for an algorithm that provides a canonical string for a given colored graph. Ie. an algorithm that returns a string for a graph, such that two graphs get the same string if and only if they are isomorphic.

In particular, I'm looking for a simple algorithm that is easy to implement with a reasonable performance on most graphs (worst case super-polynomial, of course). I'm expecting small graphs, so performance doesn't have to be stellar, just good enough.

Unfortunately, most things I've found are highly complex and more interested in expressing deep mathematical connections than simply describing the algorithm. I'm afraid I don't have the time to dive that deep. Can anyone give me a shortcut?

I'm hoping for something like the Floyd-Warshall algorithm. Not optimal, but good enough, and easy to implement.

Brendan McKay and Adolfo Piperno have written a survey paper regarding this question in 2013. They present several efficient computer programs that canonicalize many graphs faster than you would imagine. There is no need (and no point) in implementing these algorithms yourself - they are available online, even as source code.

StackExchange Computer Science Q#14354, answer score: 6