  We perform electrical transport measurements in graphene with several sample
geometries. In particular, we design ``invasive'' probes crossing the whole
graphene sheet as well as ``external'' probes connected through graphene side
arms. The four-probe conductance measured between external probes varies
linearly with charge density and is symmetric between electron and hole types
of carriers. In contrast measurements with invasive probes give a strong
electron-hole asymmetry and a sub-linear conductance as a function of density.
By comparing various geometries and types of contact metal, we show that these
two observations are due to transport properties of the metal/graphene
interface. The asymmetry originates from the pinning of the charge density
below the metal, which thereby forms a p-n or p-p junction depending on the
polarity of the carriers in the bulk graphene sheet. Our results also explain
part of the sub-linearity observed in conductance as a function of density in a
large number of experiments on graphene, which has generally been attributed to
short-range scattering only.
