Local topological features of robust supply networks

TL;DR

This paper investigates the structural properties of supply networks, revealing that certain subgraph patterns are key to their robustness and providing insights for designing more resilient supply systems.

Contribution

It introduces a minimal abstract model of supply networks, demonstrating the role of specific subgraph motifs in system robustness and offering a blueprint for improving real-world supply network resilience.

Findings

Robust networks are composed of specific subgraph sets.

Vulnerable networks have different subgraph compositions.

Network motifs are indicative of network robustness.

Abstract

The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting upon such a system, even formulating an appropriate research question to address this topic is non-trivial. Here we present an abstraction of a supply and distribution system leading to a minimal model, which only retains stylized facts of the systemic function and, in this way, allows us to investigate the generic properties of robust supply networks. On this level of abstraction, a supply and distribution system is the strategic use of transportation to eliminate mismatches between production patterns (i.e., the amounts of goods produced at each production site of a company) and demand patterns (i.e., the amount of goods consumed at each location). When creating networks based on this paradigm and furthermore requiring the robustness of the system with respect to the loss of transportation routes (edge of the network) we see that robust networks are built from specific sets of subgraphs, while vulnerable networks display a markedly different subgraph composition. Our findings confirm a long-standing hypothesis in the field of network science, namely, that network motifs -- statistically over-represented small subgraphs -- are informative about the robust functioning of a network. Also, our findings offer a blueprint for enhancing the robustness of real-world supply and distribution systems.