Identifying Self-Amplifying Hypergraph Structures through Mathematical Optimization

TL;DR

This paper introduces a novel optimization-based framework to identify self-amplifying hypergraph structures, crucial for understanding propagation in complex systems, with applications demonstrated in chemical reaction networks.

Contribution

It defines the maximal amplification factor for hypergraphs and develops an exact iterative algorithm to identify subhypergraphs that maximize this measure.

Findings

Successfully identified autocatalytic subnetworks in chemical systems

Demonstrated the effectiveness of the optimization approach on synthetic instances

Provided insights into propagation mechanisms in complex hypergraph models

Abstract

In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the maximal amplification factor, a metric that captures how effectively a subhypergraph contributes to its own amplification. We then develop an optimization-based methodology to compute this measure. Building on this foundation, we tackle the problem of identifying the subhypergraph maximizing the amplification factor, formulating it as a mixed-integer nonlinear programming (MINLP) problem. To solve it efficiently, we propose an exact iterative algorithm with proven convergence guarantees. In addition, we report the results of extensive computational experiments on realistic synthetic instances, demonstrating both the relevance and effectiveness of the proposed approach. Finally, we present a case study on chemical reaction networks, including the Formose reaction and E. coli core metabolism, where our framework successfully identifies known and novel autocatalytic subnetworks, highlighting its practical relevance to systems chemistry and biology.