Two‐route flows in an undirected flow network

Abstract This paper defines anew the maximum two‐route flow as a measure to represent the relation between two vertices in the flow network. The maximum two‐route flow corresponds to the maximum number of communication channels that are composed of two‐route paths between two terminals in a communication network. The ℱ‐rings that can be composed simultaneously, containing the considered two vertices, is defined as the maximum two‐route flow between those two vertices. It is shown in this paper that a theorem exists for the maximum two‐route flow similar to the max‐flow min‐cut theorem for the ordinary flow.