Some clarification about quasirandom graphs

Why quasirandom?
When we first started our work on quasi-random graphs in 1988, the term people mostly used was pseudo random, which did not have a definite meaning (and still doesn't). We chose the name quasirandom because of the following two reasons. Some words of caution! Remarks
  • There are two ways to define relations between various properties of graphs
  • The (basic) equivalence class of quasirandom graphs
  • Quasirandom heirarchy can be for any combinatorial structures such as graphs, hypergraphs, tournaments, permutations ...
  • Lecture notes on quasirandom graphs ---- Tim Gowers' lecture notes, Fan Chung's lecture notes.
  • Quasirandom graphs in book chapters ---- Alon/Spencer, Handbook of Combinatorics; surveys --- Mohar, Komlos/Simonovitz , Merris,
  • Graph limits is one area that was influenced by quasirandom graphs. The related references can be found in Lovasz' book on graph limits.

    Clarification of several terminologies that are often misused.
    (Of course, it is much preferred not to use the same name for two different properties that are NOT equivalent.)
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