# graph(LeafTree) -- convert a LeafTree to Graph

## Description

This converts a LeafTree representation of a tree into a Graph.

The internal vertices of a LeafTree are not named, so each vertex is specified by the partition of the set of leaves formed by removing the vertex. Each partition is given as a List of Sets.

 i1 : T = leafTree(4,{{0,1}}) o1 = {{0, 1, 2, 3}, {set {0, 1}, set {0}, set {1}, set {2}, set {3}}} o1 : LeafTree i2 : G = graph T o2 = Graph{set {set {0, 1, 2}} => {set {set {0, 1}, set {2}, set {3}}} } set {set {0, 1, 3}} => {set {set {0, 1}, set {2}, set {3}}} set {set {0, 1}, set {2}, set {3}} => {set {set {0, 1, 2}}, set {set {0, 1, 3}}, set {set {0}, set {1}, set {2, 3}}} set {set {0, 2, 3}} => {set {set {0}, set {1}, set {2, 3}}} set {set {0}, set {1}, set {2, 3}} => {set {set {0, 1}, set {2}, set {3}}, set {set {0, 2, 3}}, set {set {1, 2, 3}}} set {set {1, 2, 3}} => {set {set {0}, set {1}, set {2, 3}}} o2 : Graph i3 : adjacencyMatrix G o3 = | 0 1 1 1 0 0 | | 1 0 0 0 0 0 | | 1 0 0 0 0 0 | | 1 0 0 0 1 1 | | 0 0 0 1 0 0 | | 0 0 0 1 0 0 | 6 6 o3 : Matrix ZZ <--- ZZ