Nowadays, society urgently requires new technologies and new solutions for a clean and efficient public road transport system to achieve more sustainable cities. However, in this process towards climate-neutrality, selecting the best policy, strategy, etc. is a critical and key issue that must be carefully addressed. Currently, there is a lack of management tools that help decision making in transport systems. Graph theory is a well-known technique that has been successfully applied for solving complex and real-life problems. It graphically and easily models relations between objects allowing deep analysis of their features and dependencies. In this work, a novel methodology based on graph theory is proposed for analyzing the performance and improvements that different technologies and/or strategies can bring to public urban transport systems. Specifically, the public bus transport network of the city of Barcelona is modeled as a directed graph G = (V, E), where the vertices represent locations of the route and the edges the route traversed between two locations. Moreover, the edges of the proposed graph are weighted according to different characteristics of these segments, e.g. distance, traveling time, energy required, pollutants emitted, etc. Results show that the proposed methodology properly models the public urban transport systems and allows to gain insights through the visualization and the comparison of the performance of a given strategy/technology.