The coordination assembly of 1,3,5-trispyridylbenzene with Cu on a Au(111) surface has been investigated by scanning tunneling microscopy under ultrahigh vacuum conditions. An open two-dimensional (2D) metal-organic network of honeycomb structure is formed as the 2D network covers partial surface. Upon the 2D network coverage of the entire surface, further increment of molecular density on the surface results in a multistep nonreversible structural transformation in the self-assembly. The new phases consist of metal-organic networks of pentagonal, rhombic, zigzag, and eventually triangular structures. In addition to the structural change, the coordination configuration also undergoes a change from the two-fold Cu-pyridyl binding in the honeycomb, pentagonal, rhombic and zigzag structures to the three-fold Cu-pyridyl coordination in the triangular structure. As the increment of molecular packing density on the surface builds up intrinsic in-plane compression pressure in the 2D space, the transformation of the structure, as well as the coordination binding mode, is attributed to the in-plane compression pressure. The quantitative structural analysis of the various phases upon molecular density increment allows us to construct a phase diagram of network structures as a function of the in-plane compression.