Apply the concept of parallel edges in a graph by providing an example scenario where parallel edges are relevant.

Sure! Let's consider a scenario where parallel edges are relevant in a graph. Imagine we have a transportation network graph that represents different routes between cities. Each edge in the graph represents a direct connection between two cities.

Now, let's say we have two cities, A and B, that are connected by multiple transportation routes. For example, there might be a direct road between A and B, as well as a train route between the same cities. In this case, we can represent these two connections as parallel edges in the graph.

By having parallel edges, we can capture the different modes of transportation available between cities A and B. This information can be useful for various purposes, such as calculating the shortest path between two cities considering different modes of transportation or analyzing the efficiency of different routes based on factors like cost or travel time.

In summary, parallel edges in a graph are relevant when we want to represent multiple connections between the same pair of vertices, allowing us to capture different aspects or modes of a relationship in the graph.