Accessibility, robustness, and connectivity are the salient structural properties of networks. The labelling of networks with numeric numbers using the parameters of edge or vertex weights plays an eminent role in the study of the aforesaid properties. The systems interlinked in a network are transformed into a graphical network, and specific numeric labels assigned to the converted network under certain rules assist us in the regulation of data traffic, bandwidth, and coding/decoding of signals. Two major classes of such network labellings are magic and antimagic. The notion of supera,0edge-antimagic labelling on networks was identified in the late nineties. The present article addresses supera,0edge antimagicness of union of the networks’ starSn, the pathPn, and copies of paths and the rooted product of cycleCnwithK2,m. We also provide supera,0edge-antimagic labelling of the rooted product of cycleCnand planar pancyclic networks. Further, we design a supera,0edge-antimagic labelling on a pancyclic network containing chains ofC6and three different symmetrically designed lattices. Moreover, our findings have also been recapitulated in the shape of 3-Dplots and tables.