Is there a method to calculate something like general \"similarity score\" of a string? In a way that I am not comparing two strings together but rather I get some number (h
Your idea sounds like ontology but applied to whole phrases. The more similar two phrases are, the closer in the graph they are (assuming you're using weighted edges). And vice-versa: non similar phrases are very far from each other.
Another approach, is to use Fourier transform to get sort of the 'index' for a given string (it won't be a single number, but always). You may find little bit more in this paper.
And another idea, that bases on the Levenshtein distance: you may compare n-grams that will give you some similarity index for two given phrases - the more they are similar the value is closer to 1. This may be used to calculate distance in the graph. wrote a paper on this a few years ago, if you'd like I can share it.
Anyways: despite I don't know the exact solution, I'm also interested in what you'll came up with.