As well as direction, relationships can also carry more information. Indeed, in a road network for instance, not all streets have the same importance in a routing system. They have different lengths or occupancy during peak hours, meaning the travel time will be very different from one street to another. The way to model this fact with graphs is to assign a weight to each edge:
In the weighted graph, relationships have weights 16 and 4
Algorithms such as shortest path algorithms take this weight into account to compute a shortest weighted path.
This is not only important for road networks. In a computer network, the distance between units may also have its own importance in terms of connection speed. In social networks, distance is often not the most important property to quantify the strength of a relationship, but we can think of other metrics. For instance, how long have those two people been connected? Or when was the last time user A reacted to a post of user B?
