Pulsar wind nebulae (PWNe) are a source of very high energy radiation that can reach up to tera-electron volts and even peta-electron volts. Our work uses the pulsar tree, a graph theory tool recently presented to analyze the pulsar population and select candidates of interest. We aim to discover detectable PWNe. We also aim to test to what extent the pulsar tree is able to group detectable PWNe despite only considering the intrinsic properties of pulsars. We selected four pulsars as tera-electron volt PWNe candidates based on their positions in the pulsar tree. Using observed and assumed ranges of values for relevant parameters, we anticipated the possible spectral energy distributions of the PWNe of four pulsars (PSR J1208-6238, J1341-6220, J1838-0537, and J1844-0346) via a detailed time-dependent leptonic model that was already found to be appropriate for describing almost all other detected nebulae. We estimated the likelihood of detection for the four candidates we studied by comparing the TeV fluxes predicted by the possible models with the sensitivities of different observatories. In doing so, we provide context for analyzing the advantages and caveats of using the pulsar tree position as a marker for properties that go beyond the intrinsic features of pulsars that are considered in producing the pulsar tree.