80% of crime is committed by 20% of criminals. Intriguing, right?
Now you feel compelled to read the rest of this post. It’s all thanks toVilfredo Pareto,an influential Italian economist. After two decades of working as a railway engineer, he eventually turned to investigating the study of economics. One of his most recognisable notations was his discovery of the 80/20 concept. Besides being an academic, he spent a substantial amount of time in the garden, where he discovered that 80% of his peas were being produced by only 20% of his peapods. Maddy put foreword another of Pareto’s findings; that 80% of Italy’s land was owned by 20% of the population, and in a modern context, 80% of links on the web point to only 20% of webpages. Pareto’s principle has now turned into Murphy’s Law of management, which suggests that 80% of profits are produced by 20% of employees.
The webpage example propels what the bulk of this reading was about; the concept of a mathematical expression called a power law. Laura provides a great summary of this concept, as well as being in agreement with Maddy and myself that it was a little confusing. A simple way of explaining the concept is through the accompanying image, outlining the comparison between bell curves and power distribution. Power laws are very different to bell curves. A power law distribution has no peak; rather it is a continuously decreasing curve, implying that many small events coexist with a few large events. The numerous tiny events coexist with a few very large ones. What Laura makes of it, is that Networks like that of the Internet, instead of following a random structure as previously thought, actually follow a power-law distribution. How this was discovered this was through a ‘little robot’, which found that there were only a ‘few online nodes with an extraordinary amount of links’. Laura sees this as logical, and unsure of why it was such a surprise. I tend to agree as when I think of the Internet I think of major cites, or ‘hubs’ such as Google, Wikipedia, and Facebook, and then outward links from there.
The 80/20 rule also roughly applies to Hollywood, where 80% of Hollywood links are connected to about 30 percent of actors. The number of actor associates to x other actors decays in the system of a power law. There are a restricted number of A-level celebrities, whereas the amount of people who have ever made an appearance as an extra are multitudes higher than the notable movie stars. Take Kevin Bacon as an A-level example. Michael discusses him as an example of a dense connector within the industry by presenting the Oracle of Kevin Bacon theory. He also touches on the comedic duo of Hamish and Andy, and their take on the Bacon number.
To compare of random network and a power-law degree distribution, a clever analogy is a US roadmap compared to Airways route map. In the road map, the cities are nodes, while highways and roads are links. The US airways map shows the alternative. There are significantly larger airports which serve to almost all places in the US; Chicago, Dallas, Denver, Atlanta, and NY. But the vast majority are tiny. A few hubs connect hundreds small airports, which is characteristic of the Power Law distribution