How does the Dijkstra Algorithm handle graphs with self-loops?

The Dijkstra Algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. When it comes to graphs with self-loops, which are edges that connect a node to itself, the Dijkstra Algorithm handles them in a specific way.

In the Dijkstra Algorithm, each node is assigned a tentative distance value, which represents the shortest distance from the source node to that particular node. Initially, all nodes except the source node are assigned an infinite distance value. The algorithm then iteratively selects the node with the smallest tentative distance and updates the distances of its neighboring nodes.

When it encounters a self-loop in the graph, the Dijkstra Algorithm treats it as any other edge. However, it is important to note that self-loops can potentially cause issues in the algorithm if not handled properly. This is because the algorithm may get stuck in an infinite loop if the self-loop has a negative weight.

To handle self-loops, the Dijkstra Algorithm typically checks if the tentative distance of the neighboring node, which is connected by the self-loop, can be improved by considering the self-loop. If the tentative distance can be improved, the algorithm updates the distance value and continues with the iteration.

However, if the self-loop has a negative weight, the Dijkstra Algorithm may not produce correct results. This is because the algorithm assumes that the shortest path between two nodes does not contain any negative-weight cycles. In the presence of negative-weight cycles, the algorithm may get trapped in an infinite loop, as it keeps finding shorter paths by repeatedly traversing the negative-weight cycle.

In summary, the Dijkstra Algorithm handles graphs with self-loops by treating them as any other edge. It checks if the tentative distance of the neighboring node can be improved by considering the self-loop and updates the distance value accordingly. However, if the self-loop has a negative weight, the algorithm may not produce correct results and can potentially get stuck in an infinite loop.