Description: Arc length in the context of data graphs refers to the distance between two vertices in a weighted graph, represented by the weight of the arc connecting them. This concept is fundamental in graph theory, where vertices represent nodes or points of interest and arcs represent the connections or relationships between them. Arc length allows quantifying the ‘distance’ or ‘cost’ of moving from one vertex to another, which is crucial for solving optimization and search problems in graphs. In a weighted graph, each arc has an associated value that can represent different metrics, such as time, cost, physical distance, or any other relevant measure. Arc length is essential for algorithms like Dijkstra’s or Bellman-Ford, which are used to find the shortest path between two nodes. Additionally, this concept applies in various fields, such as transportation networks, social network analysis, and route optimization, where understanding distances between points is key for making efficient decisions.
