Design Principles for Reproducible Networks

Abstract: From protein complexes to electronic circuits, many natural and engineered systems function only if assembled in an exact, reproducible fashion. The structure of each of these systems can be understood as a network, yet network science lacks the mechanisms to consistently reproduce exact topologies, focusing instead on generating network ensembles. We introduce the framework of network design where we encode the local constraints obeyed by a system's building blocks in a design set, and derive the Unigraphical Design Theorem, which determines when these constraints guarantee reproducible assembly into a unique structure, a process we call unigraphical assembly. For systems whose design sets do not specify a unique outcome, we identify guided assembly as a second route to reproducibility, in which temporal ordering decomposes construction into unigraphical steps. Applying these results to 3,618 reproducible systems, including protein complexes, molecules, and robots, we classify those that undergo unigraphical assembly and those that require guided assembly. We further identify a diversity-redundancy boundary that explains how systems trade component variety for structurally interchangeable parts while retaining unique assembly. Finally, we experimentally test the theory using 3D-printed components to re-engineer generative construction sets into systems that assemble unigraphically into prescribed topologies. Network design thus reframes reproducibility as a mathematically testable property of real networks, opening a route to the rational engineering of complex systems.