Given a polarizable ℤ-variation of Hodge structures VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS over a complex smooth quasi-projective base VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS, a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional Hodge tensors appear) is a countable union of irreducible algebraic subvarieties of VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS, called the special subvarieties for VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS. Our main result in this paper is that, if the level of VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS is at least 3, this Hodge locus is in fact a finite union of such special subvarieties (hence is algebraic), at least if we restrict ourselves to the Hodge locus factorwise of positive period dimension (Theorem 1.5). For instance the Hodge locus of positive period dimension of the universal family of degree VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS smooth hypersurfaces in VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS, VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS, VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS and VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS, is algebraic. On the other hand we prove that in level 1 or 2, the Hodge locus is analytically dense in VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS as soon as it contains one typical special subvariety. These results follow from a complete elucidation of the distribution in VSSVVdPCn+1n≥3d≥5(n,d)≠(4,5)SanS of the special subvarieties in terms of typical/atypical intersections, with the exception of the atypical special subvarieties of zero period dimension.