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We demonstrate that quantum correlations can emerge from the statisticalcorrelations of random discrete models, without an a priori assumption that therandom models are quantum mechanical in nature, that is without consideringsuperpositions of the random structures. We investigate the correlationsbetween the number of neighbors(degree) for pairs of vertices in Erdos-Renyiuniform random graphs. We use the joint probabilities for the appearance ofdegree numbers between the vertices in the pairs, in order to calculate therespective Bell's inequalities. We find that the inequalities are violated forsparse random graphs with ratio of edges over vertices $R<2$, signifying theemergence of quantum correlations for these random structures. The quantumcorrelations persist independently of the graph size or the geodesic distancebetween the correlated vertices. For $R>2$, as the graph becomes denser byadding more edges between its vertices, the Bell's inequalities are satisfiedand the quantum correlations disappear. Relations to our previous worksconcerning the emergence of spacetime and its geometrical properties fromuniform random graphs, are also briefly discussed.

Violation of Bell's inequalities in uniform random graphs