The mechanical and electrical properties of a direct-spun carbon nanotube mat are measured. The mat comprises an interlinked random network of nanotube bundles, with approximately 40 nanotubes in a bundle. A small degree of in-plane anisotropy is observed. The bundles occasionally branch, and the mesh topology resembles a 2D lattice of nodal connectivity slightly below 4. The macroscopic in-plane tensile response is elasto-plastic in nature, with significant orientation hardening. In-situ microscopy reveals that the nanotube bundles do not slide past each other at their junctions under macroscopic stain. A micromechanical model is developed to relate the macroscopic modulus and flow strength to the longitudinal shear response of the nanotube bundles. The mechanical and electrical properties of the mat are compared with those of other nanotube arrangements over a wide range of density.