S8.10- Centros y excentricidades | 45/49 | UPV

Title: S8.10 - Centers and Eccentricities Auto-description: This video addresses the solution to location problems, specifically the optimal location of a hospital in a region. Concepts such as center, eccentricity, and distances in a weighted graph are introduced, mentioning important properties of a distance function such as positivity, identity, and the triangle inequality. The eccentricity of a vertex is defined as the maximum distance to any other vertex, and how to calculate it is explained by assigning a weight of one to edges in unweighted graphs. Then, the terms diameter and radius of a graph are introduced, establishing that the radius is always less than or equal to the diameter, which in turn is less than or equal to two times the radius. These measures are calculated using the eccentricities of the vertices. The center of a graph is defined as the set of vertices with the minimum eccentricity. The video continues by modeling a real-life hospital location problem using a weighted graph with vertices representing towns and edges simulating the roads between them, assigning travel times as weights. The eccentricities of the towns are calculated to determine the location with the lowest eccentricity, i.e., the most central location. Following the minimum eccentricity criterion, it is concluded that the hospital should be located in El Viso, offering the shortest maximum access time for nearby towns. Finally, it is anticipated that similar problems for the location of multiplex cinemas and residential areas will be addressed in future videos. Author: José Alberto Conejero Casares Course: This video is 45/49 of the MOOC course Applications of Graph Theory to Real Life II | Universitat Politècnica de València (UPV).    • MOOC Aplicaciones de la Teoría de Grafos a...   Polytechnic University of Valencia (UPV): https://www.upv.es More videos at:    / valenciaupv   Access our MOOCs: https://upvx.es #