  We study a class of growth algorithms for directed graphs that are candidate
models for the evolution of genetic regulatory networks. The algorithms involve
partial duplication of nodes and their links, together with innovation of new
links, allowing for the possibility that input and output links from a newly
created node may have different probabilities of survival. We find some
counterintuitive trends as parameters are varied, including the broadening of
indegree distribution when the probability for retaining input links is
decreased. We also find that both the scaling of transcription factors with
genome size and the measured degree distributions for genes in yeast can be
reproduced by the growth algorithm if and only if a special seed is used to
initiate the process.
