Now that we know how to properly search a graph, how can we use these skills in real life?

One of the most common applications of graph searches is to find the shortest distance between vertices. Finding this distance has a variety of applications such as finding the optimal route to a destination or transferring data in a computer network.

Take a look at the graph below. Finding the shortest path between vertex A and vertex E may seem easy in your brain, but telling a computer how to find it is a bit more complicated.

Fortunately, there is an algorithm that computes the shortest distance from a given vertex to the rest of the vertices in a graph. This is called ** Dijkstra’s Algorithm**.

Dijkstra’s Algorithm works as following:

- Instantiate a dictionary that will eventually map vertices to their distance from the start vertex
- Assign the start vertex a distance of 0 in a min heap
- Assign every other vertex a distance of infinity in a min heap
- Remove the vertex with the smallest distance from the min heap and set that to the current vertex
- For the current vertex, consider all of its adjacent vertices and calculate the distance to them as
**(distance to the current vertex) + (edge weight of current vertex to adjacent vertex)**. - If this new distance is less than the current distance, replace the current distance.
- Repeat 4 and 5 until the heap is empty
- After the heap is empty, return the distances

That may seem confusing! Be sure to check out the video in order to better visualize this algorithm.