Iterated Global Models for Complex Networks

Abstract

We introduce the Iterated Global model as a deterministic graph process that simulates several properties of complex networks. In this model, for every set $S$ of nodes of a prescribed cardinality, we add a new node that is adjacent to every node in $S$. We focus on the case where the size of $S$ is approximately half the number of nodes at each time-step, and we refer to this as the half-model. The half-model provably generate graphs that densify over time, have bad spectral expansion, and low diameter. We derive the clique, chromatic, and domination numbers of graphs generated by the model.