The Signatures of Ideal Flow Networks

TL;DR

This paper introduces Ideal Flow Networks (IFNs), a mathematical framework that uses network signatures derived from canonical cycles to analyze flow properties and reconstruct network flows.

Contribution

It presents a novel method to decompose IFNs into signatures and reconstruct them, enabling flow analysis through string manipulations.

Findings

Network signatures can be used to derive flow metrics.

IFNs can be reconstructed from signatures via assignment and merging.

The approach allows testing for irreducibility and flow properties.

Abstract

An Ideal Flow Network (IFN) is a strongly connected network where relative flows are preserved (irreducible premagic matrix). IFN can be decomposed into canonical cycles to form a string code called network signature. A network signature can be composed back into an IFN by assignment and merging operations. Using string manipulations on network signatures, we can derive total flow, link values, sum of rows and columns, and probability matrices and test for irreducibility.