Are self-organizing biochemical networks emergent?

Abstract
Biochemical networks are often called upon to illustrate emergent properties of living systems. In this contribution, I question such emergentist claims by means of theoretical work on genetic regulatory models and random Boolean networks. If the existence of a critical connectivity K_c of such networks has often been coined “emergent” or “irreducible”, I propose on the contrary that the existence of a critical connectivity K_c is indeed mathematically explainable in network theory. This conclusion also applies to many other types of formal networks and weakens the emergentist claim attached to bio-molecular networks, and by extension to living systems.