Description: An edge-weighted graph is a mathematical structure consisting of a set of nodes (or vertices) connected by edges, where each edge has an associated numerical value, known as weight. This weight can represent various characteristics, such as distance, cost, time, or any other measure that one wishes to quantify in the context of the problem being modeled. The main feature of an edge-weighted graph is that it allows for more complex and precise analyses compared to an unweighted graph, as decisions and algorithms can be based on these numerical values. For example, in a graph representing a transportation network, the weights of the edges could indicate the distance between points or the estimated travel time. This structure is fundamental in graph theory and is used in a variety of algorithms, such as Dijkstra’s or the Floyd-Warshall algorithm, which allow for finding optimal paths and solving optimization problems. In summary, edge-weighted graphs are powerful tools in the representation and analysis of complex relationships across various disciplines, from computer science to logistics and engineering.
