This paper introduces one-dimensional (1D) limited periodic multi-connected vacuum optical waveguide networks (LPMVOWN), a fascinating class of photonic bandgap structures designed to produce Dirac cones. Unlike previously explored materials such as graphene, metamaterials, photonic crystals, and phononic crystals, optical waveguide networks produce a sequence of Dirac cones while also exhibiting quantum properties in the angular frequencies corresponding to these cone points. We used the topological translational periodicity inherent in optical waveguide networks to establish analytical relationships governing the angular frequency, slope, and number of Dirac cones generated by the system. These relationships are used to elucidate how parameters like the waveguide length ratio of the units, the number of waveguide connections, and the waveguide material influence these properties. This analysis improves our understanding of linear, degenerate, and concatenated energy band structures, as well as their potential applications. Furthermore, it offers valuable insights for enhancing the control of electromagnetic wave propagation and provides experimentalists with greater convenience and flexibility in their research endeavours.