Seeking carbon phases with versatile properties is one of the fundamental goals in physics, chemistry, and materials science. Here, based on the first-principles calculations, a family of three-dimensional (3D) graphene networks with abundant and fabulous electronic properties, including rarely reported dipole-allowed truly direct band gap semiconductors with suitable band gaps (1.07–1.87 eV) as optoelectronic/photovoltaic materials and topological nodal-ring semimetals, are proposed through stitching different graphene layers with acetylenic linkages. Remarkably, the optical absorption coefficients in some of those semiconducting carbon allotropes express possibly the highest performance among all of the semiconducting carbon phases known to date. On the other hand, the topological states in those topological nodal-ring semimetals are protected by the time-reversal and spatial symmetry and present nodal rings and nodal helical loops topological patterns. Those newly revealed carbon phases possess low formation energies and excellent thermodynamic stabilities; thus, they not only host a great potential in the application of optoelectronics, photovoltaics, and quantum topological materials etc., but also can be utilized as catalysis, molecule sieves or Li-ion anode materials and so on. Moreover, the approach used here to design novel carbon allotropes may also give more enlightenments to create various carbon phases with different applications.