"Non random graphs"

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In my recent study about random graphs, I learned that there are numerous models:Bernoulli, Binomial, Watts-Strogatz, Barabasi-Albert, exponential models...etc. Now I have an idea about random graphs, what I have a problem with are "non random graphs", I can't picture them. Can anybody give me an example of a "non random graphs"?

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There are millions of such graphs, just naming a few:

  • Complete Graphs,
  • Petersen Graph,
  • Queen Graphs,
  • Grötzsch Graph,
  • Mycielski Graphs,
  • ...

You can find many graphs here: Wolfram Math World