Mechanically polished high-quality longitudinal sections of the wires were carefully examined using scanning electron microscopy, scanning spreading resistance microscopy, and Raman spectroscopy. It has been found that the interior of the wires consists of ~150-nm-thick sp2 sheets forming a conductive network inside the original diamond matrix. The sp2 sheets are clustered in segments distributed quasi-periodically along the wire. Both the velocity of the laser focus translation and the pulse energy have been found to influence the thickness of the sp2 sheets and spatial arrangement of the segments. The relationship between the internal structure of the wires and their integrated resistivity is discussed.