Geodesic
Random graphs: models and asymptotic characteristics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 1, pp. 33-81

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This is a survey of known results related to the asymptotic behaviour of the probabilities of first-order properties of random graphs. The results presented in this paper are concerned with zero-one laws for properties of random graphs. Emphasis is placed on the Erdős–Rényi model of a random graph. Also considered are some generalizations of this model motivated by various problems in the theory of coding and combinatorial geometry. Bibliography: 65 titles.
Keywords: random graphs, distance graphs, limit theorems, zero-one laws, first-order properties. 
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M. E. Zhukovskii; A. M. Raigorodskii. Random graphs: models and asymptotic characteristics. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 1, pp. 33-81. http://geodesic.mathdoc.fr/item/RM_2015_70_1_a1/