Minimal spanning tree algorithm

Minimal spanning tree(MST) problem is an application of network models. Like any other operation research problem, we are intrested in finding an optimal solution to the objective function. In case of miniml spanning tree, the objective is to find the sulution that minimizes the total distance between all the nodes in the network.

The following are the stepes to be taken when solving the problem:

Choose an node in the network amnd mark it as start node. It is rcommended to use a different color to diffrenciate the node that has already been visited from the reste of the nodes
For all connections from the start node, choose the arc with minimum value and mark the end node with same color as in step 1
At this stage, we have two nodes marked as visited(start node and node in step 2). For all connections from the two nodes , choose the arc with minimum value. if there are more than one arc with minimum value, choose one of them. It doent matter which one, the end results will be the same.
Repeat the same untill all the nodes in he network have been visited.

Note:

For a network with n nodes, there is exactly n-1 arcs in the resulting minimum spanning tree.
There should not be any cycles in the spanning tree. If there i, it means that there ws a mistake in the steps

Application

Minimum spanning tree network has many applications in real life. Below are some examples

In electicity : Distribution of electricty across the cities with the goal to minimize the length of electric cables
In computer science: Distribution of internet through cables accross a network of servers

Practical example

The network consist of the following nodes and arcs. The nodes represent computer servers and the values on the arcs represent the distance between them. The task is to find the minimum spanning tree and its values.