  In this article, we discuss the random graph, Barab\'asi-Albert (BA) model,
and lattice networks from a unified view point, with the parameter $\omega$
with values $1,0,-1$ characterizing these networks, respectively. The parameter
is related to the preferential attachment of nodes in the networks and has
different weights for the incoming and outgoing links. In addition, we discuss
the correspondence between quantum statistics and the networks. Positive and
negative $\omega$ correspond to Bose and Fermi-like statistics, respectively,
and we obtain the distribution that connects the two. When $\omega$ is
positive, it is related to the threshold of Bose-Einstein condensation (BEC).
As $\omega$ decreases, the area of the BEC phase is narrowed, and disappears in
the limit $\omega=0$. When $\omega$ is negative, nodes have limits in the
number of attachments for newly added nodes (outgoing links), which corresponds
to Fermi statistics. We also observe the Fermi degeneracy of the network. When
$\omega=-1$, a standard Fermion-like network is observed. Fermion networks are
realized in the cryptocurrency network "Tangle."
