Epoxidized natural rubber-graphene (ENR-GE) composites with segregated GE networks were successfully fabricated using the latex mixing combined in situ reduced technology. The rheological behavior and electrical conductivity of ENR-GE composites were investigated. At low frequencies, the storage modulus (G') became frequency-independent suggesting a solid-like rheological behavior and the formation of GE networks. According to the percolation theory, the rheological threshold of ENR-GE composites was calculated to be 0.17 vol%, which was lower than the electrical threshold of 0.23 vol%. Both percolation thresholds depended on the evolution of the GE networks in the composites. At low GE concentrations (<0.17 vol%), GE existed as individual units, while a "polymer-bridged GE network" was constructed in the composites when GE concentrations exceeded 0.17 vol%. Finally, a "three-dimensional GE network" with percolation conductive paths was formed with a GE concentration of 0.23 vol%, where a remarkable increase in the conductivity of ENR-GE composites was observed. The effect of GE on the atom scale free-volume properties of composites was further studied by positron annihilation lifetime spectroscopy and positron age momentum correlation measurements. The motion of ENR chains was retarded by the geometric confinement of "GE networks", producing a high-density interfacial region in the vicinity of GE nanoplatelets, which led to a lower ortho-positronium lifetime intensity and smaller free-volume hole size.