The covalent linking of acetylenes presents an important route for the fabrication of novel carbon-based scaffolds and two-dimensional materials distinct from graphene. To date few attempts have been reported to implement this strategy at well-defined interfaces or monolayer templates. Here we demonstrate through real space direct visualization and manipulation in combination with X-ray photoelectron spectroscopy and density functional theory calculations the Ag surface-mediated terminal alkyne C(sp)-H bond activation and concomitant homo-coupling in a process formally reminiscent of the classical Glaser-Hay type reaction. The alkyne homo-coupling takes place on the Ag(111) noble metal surface in ultrahigh vacuum under soft conditions in the absence of conventionally used transition metal catalysts and with volatile H(2) as the only by-product. With the employed multitopic ethynyl species, we demonstrate a hierarchic reaction pathway that affords discrete compounds or polymeric networks featuring a conjugated backbone. This presents a new approach towards on-surface covalent chemistry and the realization of two-dimensional carbon-rich or all-carbon polymers.