  We obtained Pearson's coefficient of strongly correlated recursive networks
growing by preferential attachment of every new vertex by $m$ edges. We found
that the Pearson coefficient is exactly zero in the infinite network limit for
the recursive trees ($m=1$). If the number of connections of new vertices
exceeds one ($m>1$), then the Pearson coefficient in the infinite networks
equals zero only when the degree distribution exponent $\gamma$ does not exceed
4. We calculated the Pearson coefficient for finite networks and observed a
slow, power-law like approach to an infinite network limit. Our findings
indicate that Pearson's coefficient strongly depends on size and details of
networks, which makes this characteristic virtually useless for quantitative
comparison of different networks.
