The branching of trees, the spread of river deltas, snowflakes, blood vessels, coastlines, and share price charts all show self-similar patterns that repeat when you examine them more closely. And, as you may have guessed, so does the internet.
Mathematically speaking, self-similarity can be expressed as a power law, where one quantity varies as a power of the other regardless of scale—hence “scale free.” Such distributions are known as “long tail” or “following the 80-20 rule.” Coffee grounds can be modeled as a three-dimensional network composed of granules and gaps, the “clumpyness” of which follows a power law. Web hyperlinks are the same. Barabasi and Albert17 put forward a model based on preferential attachment to explain this. The more links a website has, the more visible the site is, and so the more likely it is that it will receive further links in the future. So, the preferential attachment model can be summed up as “success breeds success” or “the rich get richer.”