The expected degree distribution in transient duplication divergence models

Abstract

We study the degree distribution of a randomly chosen vertex in a duplication–divergence graph, under a variety of different generalizations of the basic model of Bhan et al. (2002) and Vázquez et al. (2003). We pay particular attention to what happens when a non-trivial proportion of the vertices have large degrees, establishing a central limit theorem for the logarithm of the degree distribution. Our approach, as in Jordan (2018) and Hermann and Pfaffelhuber (2021), relies heavily on the analysis of related birth–catastrophe processes, and couplings are used to show that a number of different formulations of the process have asymptotically similar expected degree distributions.