The Signatures of Ideal Flow Networks
Kardi Teknomo
TL;DR
The paper introduces Ideal Flow Networks (IFNs) and a cycle-based network signature as a bidirectional, string-like representation of directed, strongly connected, premagic flow systems. It formalizes two elementary cycle operations—assignment and merging—and shows how signatures decompose into, and reconstruct from, adjacency matrices through composition and decomposition, with a premier network as a baseline. Signatures yield concrete methods to compute link flows, total flow, link probabilities, and stochastic matrices, while pivots and irreducibility criteria ensure strong connectivity. The framework provides both theoretical insights and algorithmic paths for generating, analyzing, and sampling IFNs, with practical implications for efficient network analysis and synthesis.
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.