Convergence properties of optimal transport-based temporal hypernetworks

TL;DR

This paper introduces a method to extract and analyze temporal hypergraphs from optimal transport solutions, revealing unique discrete properties and potential advantages over traditional networks in representing complex transportation data.

Contribution

The paper presents a novel approach to derive temporal hypergraphs from optimal transport solutions and compares their properties to traditional networks, offering new insights into transportation principles.

Findings

Discrete hypergraph properties differ from continuous counterparts

Hypernetworks can reveal new transportation insights

Real data analysis demonstrates method effectiveness

Abstract

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of hypergraph structures. Discrete properties follow patterns that differ from those characterizing their continuous counterparts. Analyzing these patterns can bring new insights into the studied transportation principles. We also compare these higher-order structures to their network counterparts in terms of standard graph properties. We give evidence that some transportation schemes might benefit from hypernetwork representations. We demonstrate our method on real data by analyzing the properties of hypernetworks extracted from images of real systems.