How does the Dijkstra Algorithm handle graphs with parallel edges?

The Dijkstra Algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. When it comes to handling graphs with parallel edges, the Dijkstra Algorithm treats them differently compared to regular edges.

In a graph with parallel edges, there are multiple edges connecting the same pair of nodes. Each edge may have a different weight or cost associated with it. The Dijkstra Algorithm handles parallel edges by considering only the edge with the minimum weight at each step of the algorithm.

Here is a step-by-step explanation of how the Dijkstra Algorithm handles graphs with parallel edges:

1. Initialize the algorithm by setting the starting node as the current node and assigning a distance of 0 to it. Set the distance of all other nodes to infinity.

2. Visit the current node and examine all its neighboring nodes. For each neighboring node, calculate the distance from the starting node through the current node. If this distance is smaller than the previously recorded distance for that node, update the distance.

3. After examining all the neighboring nodes, mark the current node as visited and select the unvisited node with the smallest distance as the new current node. If there are multiple unvisited nodes with the same smallest distance, choose any one of them.

4. Repeat steps 2 and 3 until all nodes have been visited or the destination node has been reached.

When it comes to parallel edges, the algorithm follows these additional rules:

- When examining neighboring nodes, consider all parallel edges connecting the current node to the neighboring node.

- Calculate the distance for each parallel edge separately, taking into account the weight of that specific edge.

- If the distance through a parallel edge is smaller than the previously recorded distance for the neighboring node, update the distance.

By considering only the edge with the minimum weight at each step, the Dijkstra Algorithm ensures that it always finds the shortest path between the starting node and any other node in the graph, even in the presence of parallel edges.