Abstract: In this paper, the V-Q Jacobian matrix expression of a grid containing photovoltaics (PVs) is derived and found to have structural properties. The grid voltage stability characteristics after large-scale integration of PVs are analyzed using matrix theory. The correlation analytical results showed that the V-Q sensitivity of a single PV node grid is consistent with the inverse of the generalized short-circuit capacity, while the V-Q Jacobian matrix of multiple PV nodes grid is consistent with the imaginary part of the nodal impedance matrix. Meanwhile, with the help of matrix theory as well as algebraic graph theory, it was clear that the V-Q Jacobian matrix is block diagonally dominant and its entries are all positive. These properties explain the existing engineering understanding that increasing the reactive power output of a PV unit rose the voltage at all nodes and had a much greater impact on the voltage magnitude in the near area than in the far area. By demonstrating the decay relationship between the entries of V-Q Jacobian matrix and electrical distance, it was pointed out that with the increase of the electrical distance between PV nodes, the interaction between voltage and reactive power will decrease. Finally, the theoretical analysis in this paper was validated by actual grid examples.