# Normalised distance measure to compare distributions

Network generation parameters are to be optimised to produce spatial networks that match a given degree distribution (discrete: negative binomial) and a given continuous distance distribution (geographic distances to network neighbours: weibull). I need a possibly normalised score [0,1] to measure the distance between the empiric distributions of produced networks and given distribution functions.

• Are you referring to a (network) graph? If so, how can you have a continuous distance? Normally, you would count the number of edges to transverse to get from one node to another. – gung Sep 22 '15 at 21:51
• Thanks gung. I mean geographic distance in a spatial (social) network. I updated the question. – Sascha Sep 23 '15 at 8:16

I finally opted for the integral-based Hellinger distance since it can be easily scaled to [0,1] and is suitable for discrete and continuous distributions (also the R package distrEx provides an implementation). A valuable resource regarding the topic is a paper by Gibbs, A. & Su, F. 2002.