The transition metal is a planar metallic organic structure, and tetra-cyano-benzene is one of the most studied networks of 3D series of transition metal. Tetra-cyano-benzene behaved as a useful object in the alloy synthesis industry due to its excellency of hardness. In spintronics, the tetra-cyano-benzene demonstrate a long-range ferromagnetic connection in the erection of magnetic, which is usually behaved as the ideal entrant. To study this novel tetra-cyano-benzene structure, we use an authentic mathematical tool known as vertex-edge and edge-vertex base topological indicators and shows some physical and chemical properties in numerical form, to understand the structure deeply. In this paper, we consider the formulas of the Zagreb indicator, first Zagreb alpha indicator, first Zagreb beta indicator, second Zagreb indicator, Randic indicators, Atom bond connectivity indicator, Geometric arithmetic indicator, Harmonic indicator and Sum connectivity indicator for transition metal tetra-cyano benzene (TCB(r,s)) structure based on vertex-edge and edge-vertex degree.