In this article we map out the thickness dependence of the resistivity of individual graphene strips, from single layer graphene through to the formation of graphitic structures. We report exceptionally low resistivity values for single strips and demonstrate that the resistivity distribution for single strips is anomalously narrow when compared to bi- and trilayer graphene, consistent with the unique electronic properties of single graphene layers. In agreement with theoretical predictions, we show that the transition to bulklike resistivities occurs at seven to eight layers of graphene. Moreover, we demonstrate that the contact resistance between graphene flakes in a graphene network scales with the flake thickness and the implications for transparent conductor applications are discussed.