Coaxial and twisted pair conductive yarn structures reduce signal crosstalk between adjacent lines in woven electrical networks. A coaxial conductive yarn structure includes an inner conductive yarn having a plurality of conductive strands twisted together. An outer conductive yarn is wrapped around the inner conductive yarn. An insulating layer separates the inner and outer yarns. A twisted pair conductive yarn structure includes first and second conductive yarns, each including a plurality of conductive strands being twisted together. The first and second conductive yarns are twisted together to form a helical structure. In a woven electrical network, at least one conductor of adjacent conductive yarn structures is connected to ground to reduce signal crosstalk. Coaxial and twisted pair yarn structures may also be formed simultaneously with weaving or knitting the threads that make up the structures into a fabric.