The algorithm computes the shortest path from a starting node to all other nodes in the graph. It selects the node with the smallest known distance, updates the distances of its neighbors, and repeats this process until all nodes have been visited.

Steps of Dijkstra's Algorithm: 1. Set the distance to the source node as 0 and to all other nodes as infinity. 2. Mark the source node as visited. For all its neighbors, calculate the tentative distance using the current node’s distance. If this new distance is smaller than the previously known distance, update it. 3. Move to the unvisited node with the smallest tentative distance and repeat the process of updating distances for its neighbors. 4. Continue this process until all nodes are visited, ensuring that the shortest path to each node is found.

Example: Consider a graph where nodes represent cities and edges represent the distance between them. Starting from city A, Dijkstra's Algorithm will calculate the shortest distance to all other cities, considering the sum of edge weights in each step.

Time Complexity: The time complexity of Dijkstra's Algorithm is O((V + E) log V), where V is the number of vertices and E is the number of edges in the graph.

Limitations: Dijkstra's Algorithm does not work with graphs that have negative edge weights because the greedy approach might not always lead to the optimal solution.