I'm currently working on a research involving Graph theory. More specifically, I would like to make an analytical or theoretic connection between different characteristics of the graph (e.g. size, node degree distribution, number of nodes with degree 1, etc.) to its minimal cut. The graph is also characterized by a source and a sink for flow purposes. By minimal I mean the number of edges or sum of capacities. Relevant connections might be on the distribution of number of paths from S to T in the minimal cut, distribution of cut-sizes, etc.
I'd appreciate if someone can suggest a lead, paper or a good approach to tackle this both theoretically and analytically.
Thank you in advance for the effort,
Avner