Large-world networks and species, social, and internet collapse

A Small-World Network is found in many naturally and and artificial situations. At the other extreme, if a network is totally connected, a complete digraph? You get zero information. This can be translated into species collapse, zero advertising revenue, and others such as ineffectual internet search.

Can this happen? In animal populations a fully connected graph is when everyone is closely related. The gene pool is stagnant. That population dies. In the internet, it could happen if everyone is on FaceBook and knows everyone else, or they are on Twitter, and follows everyone else. Another example, in the Mathematical field, a complete graph would mean that everyone would have an Erdős number of 1.

Is there a graph measure that correlates to the above? The more connected the less information, an Entropy?

Information loss, heat death. Time for another Big Bang.

Updates

  • October 3, 2015: Continuing the above line of thought, perfect order leads to zero information.
  • October 5, 2015: A Zombie Apocalypse is just a food network that is maximally connected, your next meal is sitting right next to you.

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