I was just wondering if anyone knew...
Is there a field in which analysis is used to solve graph theoretic problems? I've tried quite hard to find such a thing on google but most things that turn up are related to analysis of graphs and social network analysis and the such. This is not what I want.
I know that probability theory has been used to some extant for existence proof (e.g. Erdos), but I haven't seen anything like hard core analysis being used.
There exist Analytic Number Theory, but no Analytic Graph Theory?
Is there really such a gaping vacuum?