How to Grow Your Own Trees from Cut-Set or Tie-set Matrices

The method recognizes that construction of a tree (and hence the pertinent graph) from a given matrix can be done by inspection once the pattern of its growth has been established. To this end it is only necessary that we have a mechanism, applicable to a given cut-set matrix which sorts out those rows that correspond to the outermost twigs or tips of the tree, for we can then form an abridged cut-set matrix corresponding to what is left of the total graph after the tree tips with their uniquely attached links are pruned away. This remainder again has tips which can be found and eliminated in the same way. Continuation thus reveals the desired growth pattern. Since the method cannot fail to yield a graph if its existence is compatible with the structure of the given matrk, it may be regarded as a constructive test for fulfillment of necessary and sufficient conditions.