Understanding the minimum spanning tree (MST)

Suppose we are designing our new office campus with multiple buildings interconnected to each other. If we approach the problem by considering the interconnectivity between each building, it will take a huge number of cables. However, if we could somehow connect all the buildings through a common connectivity where each building is connected to every other building with only one connection, then this solution will reduce the redundancy and cost. If we think of our buildings as vertices and the connectivity between buildings as the edges, we can construct a graph using this approach. The problem we are trying to solve is also known as the minimum spanning tree, or MST. Consider the following graph. We have 10 vertices and 21 edges. However, we can connect all 10 vertices with only nine edges (the dark line). This will...