A Max-Flow Min-Cut Theorem with Applications in Small Worlds and Dual Radio Networks

TL;DR

This paper proves a max-flow min-cut theorem applicable to certain random graphs and demonstrates its use in analyzing small world and dual radio wireless networks, providing bounds on network capacity.

Contribution

The paper introduces a max-flow min-cut theorem for random graphs with an independence-in-cut property and applies it to small world and dual radio networks.

Findings

Derived max-flow min-cut bounds for small world networks

Established the independence-in-cut property for relevant network classes

Applied theorem to dual radio wireless networks

Abstract

Intrigued by the capacity of random networks, we start by proving a max-flow min-cut theorem that is applicable to any random graph obeying a suitably defined independence-in-cut property. We then show that this property is satisfied by relevant classes, including small world topologies, which are pervasive in both man-made and natural networks, and wireless networks of dual devices, which exploit multiple radio interfaces to enhance the connectivity of the network. In both cases, we are able to apply our theorem and derive max-flow min-cut bounds for network information flow.