2025-272

A friend of yours has published a pioneering research paper in a niche area, and it has gathered several citations from other researchers. The directed graph below shows the citation relationships among papers in this area.

Your friend is extremely happy with the results, given that his Paper A is already the most influent paper in the network, with an incoming degree of 4. Curious, with your knowledge on network science, you want to understand what the probability is of a new paper citing paper A. 

You are happy with rough approximations, so you frame this problem using a copying model for a directed network. With probability \(p = 0.4\) of linking uniformly at random to an existing paper, and probability \(1 - p\) of copying a link from a random paper, what is the probability of a new paper connecting to paper A? Round to two decimal places.

a) 0.10

b) 0.20

c) 0.21

d) 0.29

e) None of the above

Original idea by: Alexandre Petrachini