Are there any graph invariants which have a reasonable chance of capturing the graph up to isomorphism? In other words, some candidates for a function $f$ such that $f(G)=f(H)$ if and only if $G$ and $H$ are isomorphic.
For instance, in the case of trees, weighted graph polynomial ($U$-polynomial) of Welsh/Noble 1999 is a candidate because no counter-example has been found. Are there such candidates for general graphs?
Clarification: I'm interested in examples of functions which capture some graph invariant, are practical to compute, and are not yet proven to assign the same value to a pair of non-isomorphic graphs