A minimum spanning tree of a road network

Networks are very common in our highly interconnected world. As an example, consider the network of communication between everyone in the world. It is frequently said that we could reach anyone though six intermediate people (six degrees of separation). Yet, our communication patterns are shaped mostly by the people in our immediate neighborhood.

When building a road network, it is important to consider who will be using it. If a regular citizen could barely live on a 170 euro monthly salary, will they eventually support building roads swallowing millions? What is the relative perceived cost of the investment and when will it eventually repay? How long will Dobri need to work to finance the road in front of his house and will he need to fall deeply into debt? These are all important questions and I have still not heard any reasonable answer to them.

We could plot the map of the country and overlay the minimum spanning tree on it to show through which cities the roads should pass. A small map segment shows a couple of big cities and the network in which they are currently connected. If you click on it, you should see the minimum spanning tree of all cities.

Despite these small defects, we see that the minimum spanning tree connects the cities relatively evenly, so it can be a useful model for the analysis of similar networks. Building a more optimal network means lower maintanence costs and reducing our resource usage.

I hope that this gave you an idea of how you could reduce the resource usage of your company. In a resource-constrained world this skill will be progressively more valued and needed. Over-investments break businesses, introduce corruption, deplete people of the resources they need for a normal life. We need to avoid them and bootstrap when possible.

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