Summary: The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups \(\mathbb{G}(\Delta)\) and \(\mathbb{G}(\Gamma)\) are quasi-isometric, then \(\mathbb{G}(\Delta)\) is a (nice) subgroup of \(\mathbb{G}(\Gamma)\) and vice-versa. We show that the conjecture holds for all known cases of quasi-isometric classification of partially commutative groups, namely for the classes of \(n\)-trees and atomic graphs. As in the classical Mostow rigidity theory for irreducible lattices, we relate the quasi-isometric rigidity of the class of atomic partially commutative groups with the algebraic rigidity, that is, with the co-Hopfian property of their \(\mathbb{Q}\)-completions.