Some Models of Reproducing Graphs: II Age Capped Vertices

In the prequel to this paper we introduced eight reproducing graph models. The simple idea behind these models is that graphs grow because the vertices within reproduce. In this paper we make our models more realistic by adding the idea that vertices have a finite life span. The resulting models capture aspects of systems like social networks and biological networks where reproducing entities die after some amount of time. In the 1940’s Leslie introduced a population model where the reproduction and survival rates of individuals depends upon their ages. Our models may be viewed as extensions of Leslie’s model-adding the idea of network joining the reproducing individuals. By exploiting connections with Leslie’s model we are to describe how many aspects of graphs evolve under our systems. Many features such as degree distributions, number of edges and distance structure are described by the golden ratio or its higher order generalisations.