Recall that edges in a graph represent a connection between the vertices. If edges establish a connection, weight can be assigned to that connection. For example, for a graph that represents a map, the weights on the edges are distances.
It is important to note that the graphical length of an edge means nothing with regard to the edge’s weight. It is purely there for visual purposes. In the implementation and the code, the visual representation is not required. In Figure 17-28, the weights tell us the distances between the cities in a graph representation of five cities. For example, graphically, the distance from City 1 and City 2 is shorter than the distance from City 2 and City 3. However, the edges indicate that the distance from City 1 to City 2 is 50 km, and the distance from City 2 to City 3 is 10 km, which is five times larger.
[…] Figure 17-28. Graph representation of five cities
The most important question for weighted edge graphs is, what is the shortest path from one node to another? There are series of shortest path algorithms for graphs. The one we discuss is Dijkstra’s algorithm.
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BAE, Sammie, 2019. JavaScript Data Structures and Algorithms: An Introduction to Understanding and Implementing Core Data Structure and Algorithm Fundamentals. Berkeley, CA: Apress : Imprint: Apress. ISBN 978-1-4842-3988-9, p. 293.
⇒ Weights