We have employed the Dirac's massless quasi-particles together with the Kubo's formalism of the linear response to study the spin transport properties by electrons in the graphene monolayer. We have calculated the electric conductivity and verified the behavior of the AC and DC currents of this system, which is a relativistic electron plasma. Our results show a superconductor behavior for the electron transport with the AC conductivity tending to infinity in the limit ω → 0. This superconductor behavior for the electron transport in the graphene is similar to one recently obtained theoretically for the spin transport in the quantum frustrated Heisenberg antiferromagnet in the honeycomb lattice, verifying so a similarity between these two different kinds of transport what can generate futures applications in the modern electronic.