  We demonstrate that quantum correlations can emerge from the statistical
correlations of random discrete models, without an a priori assumption that the
random models are quantum mechanical in nature, that is without considering
superpositions of the random structures. We investigate the correlations
between the number of neighbors(degree) for pairs of vertices in Erdos-Renyi
uniform random graphs. We use the joint probabilities for the appearance of
degree numbers between the vertices in the pairs, in order to calculate the
respective Bell's inequalities. We find that the inequalities are violated for
sparse random graphs with ratio of edges over vertices $R<2$, signifying the
emergence of quantum correlations for these random structures. The quantum
correlations persist independently of the graph size or the geodesic distance
between the correlated vertices. For $R>2$, as the graph becomes denser by
adding more edges between its vertices, the Bell's inequalities are satisfied
and the quantum correlations disappear. Relations to our previous works
concerning the emergence of spacetime and its geometrical properties from
uniform random graphs, are also briefly discussed.
