The algorithmic approach to finding the shortest path in a graph is commonly solved using graph search algorithms. The most well-known algorithm for solving this problem is Dijkstra's algorithm. Here, I will briefly explain Dijkstra's algorithm and its steps:

  1. Initialize the distance of all nodes from the source node as infinity, except for the source node itself, which has a distance of 0.

  2. Create a priority queue (min-heap) to store the nodes and their distances.

  3. Insert the source node into the priority queue.

  4. While the priority queue is not empty:

   a. Extract the node with the minimum distance from the priority queue.

   b. For each neighboring node of the extracted node:

   - Calculate the tentative distance from the source node to the neighboring node. If this distance is less than the current distance of the neighboring node, update it.

   - If the neighboring node is not yet visited, add it to the priority queue.

  5. Repeat steps 4 until the priority queue is empty.

  At the end of the algorithm, we will have the shortest distance from the source node to all other nodes in the graph. To reconstruct the shortest path, we can use an additional data structure like a parent array, which stores the previous node that leads to the current node with the shortest distance.

  Dijkstra's algorithm guarantees finding the shortest path in a graph with non-negative edge weights. However, if the graph contains negative edge weights or cycles, Dijkstra's algorithm may produce incorrect results. In such cases, other algorithms like Bellman-Ford or A* may be more suitable.

  It's also worth mentioning that there are other well-known algorithms for finding the shortest path in a graph, such as Bellman-Ford algorithm, Floyd-Warshall algorithm, and A* algorithm. The choice of algorithm depends on the specific requirements and characteristics of the problem at hand.