The accumulation of plastic debris has been a consistently alarming global issue. Plastic recycling is a viable option, but the sustainability of the recycling network is directly linked with environmental performance, which is mainly dependent on energy consumption. This work aims to provide a sustainability assessment tool by determining the ideal minimum energy requirements for a circular system, with the main driven constraint to be the thermodynamic Energy Quality Factor (exergy fraction within the energy flow). The energy quality represents the extractible energy fraction from either a material or an energy stream. The Energy Quality Pinch Analysis serves as an assessment tool for a symbiosis network, as an indication of the existing system performance from the perspective of energy. The analysis considers cascades of the energy requirements released by recycling or symbiosis processes, evaluating the minimal external energy flows: high-quality energy input and waste energy output. The method is applied for a plastic waste recycling network case study, where the energy products can be reused or recycled for various recycling pathways. The case study shows that the maximum recyclable energy is 28 %. However, if the exergy destruction rate is taken into account for fuel conversion processes, the energy quality of the sources or sinks could be reduced. Various renewable fuels with different energy quality factors can be incorporated into the system tool to evaluate the energy requirements for the plastic system.