A minimum spanning tree is a connections matrix in which all of the points are connected in a single network without any reticulate (closed) loops and in which the sum of the distances along each connection is minimal. The procedure works by starting with a single point in the “connected” group and placing the remaining points in an “unconnected” group. PASSaGE then finds the shortest distance between a point in the connected group and one in the unconnected group and connects that pair. The procedure is repeated until all of the points have been added to the network. The nearest neighbor connections are a subset of the minimum spanning tree.
Example of a minimum spanning tree. One can move from each point to any other point through the network. No connections cross and there is only a single path from each point to every other point because there are no closed loops.