The overall min-cut problem in a capacitated undirected network is well known. Recently Stoer and Wagner gave an elegant algorithm for finding such a cut. In this paper we present a parametric analysis of such a cut where the capacity of an arc {i,j} in the network is given by min{b i j ,λ}, where λ is a parameter ranging from 0 to ~. Letting function v(λ) denote the min-cut capacity, we develop an algorithm to describe v(λ) which involves at most n applications of Stoer and Wagner scheme, where n denotes the number of nodes in the network. We use v(λ) to determine an overall min-cut for multiroute flows as defined by Kishimoto. Such multi-route flows have interesting applications in communication networks.