There is utmost urgency to decarbonize the various industry sectors to keep the global temperature increase within adaptable levels. The P-graph framework is a tool that can support the network design and optimization of new and integrated decarbonization and carbon management systems. An advantage of the P-graph is the capability to determine optimal and near-optimal network solutions that aid decision-making. P-graph is commonly applied in planning supply chain networks and designing reaction pathways and mechanisms but can also be used in designing and optimizing systems to reduce carbon emissions. This work surveys the P-graph literature on decarbonization and Carbon Management Networks (CMNs). Bibliometric analysis is used to identify the trends, knowledge gaps, and potential future research areas. P-graph studies related to biomass and renewable energy are dominant research areas in this sub-area of study. Emerging topics include bio-hydrogen renewable energy, Negative Emissions Technologies (NETs), and Carbon Capture and Storage (CCS). Trend analysis suggests that P-graph approaches to biorefineries, product design, uncertainty, and risk analysis will continue to grow. Other combined techniques with P-graph such as the use of sustainability indicators, reliability and criticality analysis, multi-criterion decision analysis (MCDA), Life Cycle Optimization (LCO), and Monte Carlo simulation extend the capabilities of P-graph. A knowledge gap exists in P-graph approaches to green ammonia, solar, hydroelectric, and other renewable energy sources and products, which points to potential research opportunities.