Networks and Entropy

It being the case that most fungi form networks of cells in a bifurcated hyphal format I can't help but wonder if a "network" is an entropy directed development in the natural world. Matter and systems of matter in the universe tend to move to the lowest energy state. That being said, is a network a "lowest energy state"?

How is entropy related to networks and if we can answer that question, is the knowledge leverageable in some way?