Thank you for your answer. I forgot to mention that I am always only adding one edge. Forgive me if I’m wrong, but as far as I know, then
-1/d * degree + 1
can’t become negative when iteratively constructing the graph if d >= 2. The root starts out with weight +1 > 0 and every new vertex gets initial weight -1/d +1 > 0. And the degree can always only increase by one and so we will reach -d/d +1 = 0 and then the weight will not decrease any further. Unsure if I’ve missed something in the construction of the graph. This might not work when adding multiple edges at once, I forgot to consider that (you might “skip over the zero” in that case). I guess I will just try it out and see if there is any error.
And thank you for your addition, but yes I am quite sure that this is a random tree generating process with sufficient amounts of randomness to be interesting! (:. The usual way to formulate the attachment probability is (d - deg(v))/normalization, which is probably easier to understand. But this can be re-formulated into (-1/d deg(v) +1)/normalization which is what I’m trying to exploit here! And since igraph provides a lot of random graph generators, I figured maybe it would be interesting to provide another variant.
Lastly, I am also not sure if I understand you correctly. Due to Wikipedia, these two processes absolutely generate the same type of random tree. I think the labelling of the nodes might be the crux here.