Polymer compositions containing a polymer matrix, a graphene that is covalently bonded to the polymer matrix and metal particles are described herein. A combined concentration of the metal particles and the graphene in the polymer matrix exceeds an electrical percolation threshold. In general, the graphene has a carbon:oxygen ratio of at least about 20:1 so as to impart a high electrical conductivity thereto. The polymer compositions can be used as a lead-free solder material, in which case they can allow multiple rework operations to take place at a connection. Methods for making and using such electrically conductive polymer compositions are also described.