One interesting application of graph theory, or Ramsey theory to be more specific, is the so-called "Theorem on Friends and Strangers". It shows, using graph theoretical principles, that within any group of six or more people, at at least three must either all be mutual strangers, or mutual acquaintances. Similarly, another common application of graph theory is the so-called "six degrees of separation," which comes from the theorem in graph theory that on average, the social distance is proportional to the logarithm of the population size.
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