  A considerable success in phenomenological description of high-T$_{\rm c}$
superconductors has been achieved within the paradigm of Quantum Critical Point
(QCP) - a parental state of a variety of exotic phases that is characterized by
dense entanglement and absence of well-defined quasiparticles. However, the
microscopic origin of the critical regime in real materials remains an open
question. On the other hand, there is a popular view that a single-band $t-t'$
Hubbard model is the minimal model to catch the main relevant physics of
superconducting compounds. Here, we suggest that emergence of the QCP is
tightly connected with entanglement in real space and identify its location on
the phase diagram of the hole-doped $t-t'$ Hubbard model. To detect the QCP we
study a weighted graph of inter-site quantum mutual information within a
four-by-four plaquette that is solved by exact diagonalization. We demonstrate
that some quantitative characteristics of such a graph, viewed as a complex
network, exhibit peculiar behavior around a certain submanifold in the
parametric space of the model. This method allows us to overcome difficulties
caused by finite size effects and to identify the transition point even on a
small lattice, where long-range asymptotics of correlation functions cannot be
accessed.
