Historical Contingencies Steer the Topology of Randomly Assembled Graphs

TL;DR

This paper introduces a novel random graph model inspired by assembly theory, revealing how historical contingencies influence graph topology and enabling diverse graph ensembles with potential applications in science and engineering.

Contribution

The paper presents a new assembly-inspired random graph model and characterizes how historical contingencies shape graph properties beyond degree sequences.

Findings

Generated graphs exhibit diverse properties not predictable by degree sequences.

Historical contingencies significantly influence graph topology.

The model has potential applications in drug discovery and materials science.

Abstract

Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties, and allow for sampling from distinct ensembles. Here we introduce a new random graph model, inspired by assembly theory, and characterize the graphs it generates. We show that graphs generated using our method represent a diverse ensemble, characterized by a broad range of summary statistics, unexpected even in graphs with identical degree sequences. Finally we demonstrate that the distinct properties of these graphs are enabled by historical contingencies during the generative process. These results lay the foundation for further development of novel sampling methods based on assembly theory with applications to drug discovery and materials science.