GRAPH GRAMMAR OPERATION ‘REMOVE A LEAF NODE’ | GRAPH GRAMMAR OPERATION ‘SHRINK INTERNAL EDGE’ |
Applicable to: node A of the graph with deg(A) = 1 | Applicable to: any edge {A,B} such that deg(A) > 1 and deg(B) > 1. |
Update of the graph structure: for a given edge {A,B}, connecting nodes A and B, remove edge {A,B} and node A from the graph | Update of the graph structure: for a given edge {A,B}, connecting nodes A and B, remove {A,B}, reattach all edges connecting A with its neighbors to B, remove A from the graph. |
Update of the elasticity matrix: if B is the center of a 2-star then put zero for the elasticity of the star for B (B becomes a leaf) else do not change the elasticity of the star for B Remove the row and column corresponding to the vertex A |
Update of the elasticity matrix: The elasticity of the new star with the center in B becomes the average elasticity of the previously existing stars with the centers in A and B Remove the row and column corresponding to the vertex A |
Update of the graph injection map: all nodes besides A keep their positions. | Update of the graph injection map: B is placed in the mean position between A and B. |