  In this paper we introduce new models of random graphs, arising from Latin
squares which include random Cayley graphs as a special case. We investigate
some properties of these graphs including their clique, independence and
chromatic numbers, their expansion properties as well as their connectivity and
Hamiltonicity. The results obtained are compared with other models of random
graphs and several similarities and differences are pointed out. For many
properties our results for the general case are as strong as the known results
for random Cayley graphs and sometimes improve the previously best results for
the Cayley case.
