Compartment model on the circle

Abstract

We study the emergence of a giant component in the configuration model subject to additional constraints on the possible connections in the network. In particular, we partition a circle into compartments, and only allow edges between vertices of neighbouring compartments. We prove that under similar conditions on the degree sequence as for the standard configuration model, a giant component emerges provided the number of vertices per compartment grows quickly enough. We demonstrate the difference from the standard configuration model by providing an example with fixed compartment size where no giant component emerges, while the conditions on the degree sequence lead to a giant component in the standard configuration model.