Convergent assembly of networks with designed building blocks

Many real systems have a remarkable ability to build networks in a reproducible fashion. These networks form from building blocks each with inherent rules defining their potential connections.

Network science has introduced many generative models that, due to their inherent stochasticity, produce networks with strongly varying connectivity patterns. However, in many systems it is precisely the exact wiring that facilitates the network’s function. This raises the question of how real systems build reproducible networks from pre-designed building blocks.

We encode the role the different building blocks play in the network in the design set. This set includes information about the distribution of node types, the number of neighbors each type can have, and the specific interaction rules between the different types.

If there is only one unique network compatible with the design set, any proper assembly process must converge to that graph. We call this convergent assembly. Using the mathematical framework of unigraphs, we provide a set of conditions for convergent assembly.

We study a wide range of networks from different fields of research and determine whether their associated design sets lead to convergent assembly. For example, we look at protein complexes where nodes are proteins and links represent physical interactions between them. These complexes generally satisfy the unigraphicality conditions, raising interesting questions about the evolutionary benefits of graph topologies that are easy to assemble.