I want to compute the relationship between delay (latency) with distance and betweenness. More specifically, if I know (let's assume) that the distance and betweenness values for two different autonomous systems (one sender & one receiver) is 2 and 3 respectively, is there a formula or something like that to estimate the latency between these two ASes? I would appreciate any help.
Firstly "Latency between AS's" doesn't really make much sense as a concept. Many AS's span the globe. The latency between two geographically close points in dfferent AS's can easilly be far less than the latency between two geographically distant points in the same AS.
The default way of keeping traffic between two globe-spanning ASs local was/is to use "hot potato" routing. Basically you get the traffic out of your AS as quickly as possible and let the destination AS worry about where in the world the user is.
Some ASs may instead chose to request and respect "multi-exit discriminators" in the routing information they receive so that local traffic stays local while long distance traffic remains in the source AS for longer.
Given that AS's can range from something that sits in a single room to something that spans the globe the number of AS's involved isn't really going to be a good indication of latency either.