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We develop a hyperelastic constitutive model for graphene --- describingin-plane deformations involving both large isotropic and deviatoric strains ---based on the invariant-theoretic approach to representation of anisotropicfunctions. The strain energy density function $\psi$ is expressed in terms ofspecial scalar-valued functions of the 2D logarithmic strain tensor $ \mathbfE^{(0)}$ --- called the symmetry-invariants --- that remain invariant w.r.t.the material symmetry group of graphene, $\mathcal G = \mathcal C_{6v}$. Ourconstitutive model conforms to a larger set of \textit{ab initio}energies/stresses while introducing fewer elastic constants thanpreviously-proposed models. In particular, when the strain energy is expressedin terms of symmetry invariants, the material symmetry group is intrinsicallyincorporated within the constitutive response functions; consequently, theelastic constants (of all orders) in the formulation are \textit{a priori}independent: i.e., no two or more elastic constants are related by symmetry.This offers substantial simplification in terms of formulation as it eliminatesthe need for identifying the independent elastic constants, a task which canbecome particularly cumbersome as higher-order terms in the strain energydensity function are incorporated. We validate our constitutive model bycomputing (1) the stress and (2) the elastic stability limit for a set ofhomogeneous finite deformations --- comprising uniaxial stretch/stress alongthe armchair, and the zigzag directions; and equi-biaxial tension. The stressvalues predicted by the model are in good agreement with thedirectly-calculated \textit{ab initio} values. The elastic stability limitspredicted by acoustic tensor analysis compare well with the predictions fromphonon calculations carried out independently using linear response densityfunctional perturbation theory.