Analysis of biological networks: Real networks and random network

Social networks are amongst the first to be studied. Six degrees of separation is the theory that anyone on earth can be connected to any other person on the planet through a chain of acquaintances that has no more than five intermediaries. The theory was first proposed in 1929 by the Hungarian writer Frigyes Karinthy in a short story called Chains. In 1967, American sociologist Stanley Milgram devised a new way to test the theory, which he called ”the small-world problem”. He randomly selected people in the American Midwest to send packages to a target located in Boston, several thousand miles away. The senders knew the recipient’s name, occupation, and general location. They were instructed to send the package to a person they knew on a first-name basis who they thought was most likely, out of all their friends, to know the target personally. That person would do the same, and so on, until the package was personally delivered to its target recipient. On average, it only took between five and seven intermediaries to get each package delivered. Milgram’s findings were published in Psychology Today and inspired the phrase six degrees of separation. Social networks can be presented as a graph where: