I want to know why the distances between nodes in a minimum spanning tree seems to be rooted to the node with highest degree.
A bit of context here:
I have spatial explicit weighted network that describes the physical growth pattern of a fungal colony. Most of the nodes in this network have either degree = 1 or degree =3 (degree=2 is not possible because of biological reasons). Degree >4 are not possible except for only one (and only one) case: the center of the colony, where all edges orginally radiate.
Using the observed network, I obtained the MST (taking into account edge weights. BTW I using the mst function in igraph for R). I did this because I wanted to know how much the fungal colony differs from a MST pattern. However, I noticed that the resulting MST is essentially made up of the shortests paths between the center of the colony (that is, the only node with degree > 4) and any other node in the network. I am a biologist diving into network science, so I am now curious why is that so? why I do not get a shorthest path that does not include the node with hightest degree in the MST?