Semigroups for flows on limits of graphs

TL;DR

This paper develops a mathematical framework using semigroups and category theory to analyze flows on large or growing networks, providing a new approach to understanding dynamic processes on complex graph structures.

Contribution

It introduces a novel application of the Trotter-Kato approximation theorem combined with direct limits to study flows on expanding networks.

Findings

Established a method for approximating flows on large networks

Connected semigroup theory with graph growth models

Provided insights into the stability of flows on limits of graphs

Abstract

We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study flows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory.