The 2030 Agenda outlines a global roadmap for sustainable development, promoting prosperity while protecting the planet. Strict policies for reducing global warming are being implemented in most developed countries, with a special focus on road transport due to its significant contribution to pollutant emissions. Designing efficient and sustainable public transport systems is crucial and a complex task that requires important decision making for selecting strategies that balance sustainability, efficiency, operational cost and comfort. This work presents a graphical visualization framework that can be used as a decision support tool for analyzing public bus transport strategies. Specifically, graph theory is used to obtain structural information and descriptive parameters of the complete public bus transport of the urban area of Barcelona, and to graphically visualize it. Results show that it is a sparse but highly connected system, composed of predominantly low-degree nodes with a few central hubs in the city centre. The proposed framework allows for a realistic representation of the bus network and also facilitates quantitative and visual assessments for decision making.