The indegrees and outdegrees of pages in the web obey a power law that can be modeled by a preferred attachment process. Suppose that each web page has exactly one outgoing link. Each page is created one at a time, starting with a single page that points to itself. With probability \(p<1\), it links to one of the existing pages, chosen uniformly at random. With probability \(1-p\), it links to an existing page with probability proportional to the number of incoming links of that page. This rule reflects the common tendency for new web pages to point to popular pages. Compose a program to simulate this process and plot a histogram of the number of incoming links.

Partial solution. The fraction of pages with indegree \(k\) is proportional to \(k^{-1 /(1-p)}\).