Description: An edge-weighted network is a type of graph in which each edge (or connection) between nodes (or vertices) has an associated weight. This weight can represent different concepts, such as costs, distances, capacities, or any other quantitative measure that influences the relationship between nodes. The main characteristic of these networks is that they allow modeling situations where not only the existence of a connection is important but also the magnitude of that connection. For example, in a transportation network, nodes can represent cities, and edges can represent the roads between them, where the weight of each edge could be the distance or travel time. Edge-weighted networks are fundamental in graph theory, as they allow for more complex and realistic analyses of interconnected systems. Through specific algorithms, such as Dijkstra’s or the Floyd-Warshall algorithm, optimal paths can be found and flow analyses can be performed, making them valuable tools in various disciplines, from computer science to engineering and economics.
