Bachelor's Thesis
Project
Mathematical Modeling Capstone Project:
Guadalajara Metropolitan Area’s public transport from a graph theory perspective.
The thesis studies the public transportation network of the Guadalajara Metropolitan Area as a complex system. The analysis is carried out on two levels: the physical infrastructure layer (stops, connections, and layout) and the service layer (how people actually travel between points in the city).
Objective
Build a structural reading of the system to answer three central questions:
- How is the transport network organized.
- Which nodes or corridors are critical in the face of failures.
- How robust is the network against random interruptions and targeted attacks.
Methodology
- Modeling the network using graph theory.
- Building graphs in infrastructure space and service space.
- Calculation of topological metrics (centrality, clustering, connectivity, and diameter).
- Functional community detection.
- Simulation of vulnerability and service degradation scenarios.
Main Findings
The work identifies an important tension: the physical infrastructure shows structural fragility at articulating points, while the service network achieves greater resilience thanks to operational redundancy. In practical terms, the system is sustained more by overlapping routes than by an optimal physical topology.
Relevance
This project seeks to provide a quantitative basis for discussing urban mobility from applied mathematics, with implications for planning, investment prioritization, and systemic risk assessment in public transportation.
Repository and Access
The repository is currently open and publicly accessible on GitHub for consultation, audit, and research: