Vertex analysis defines dichotomous networks in terms of the relative frequencies of pendant ( V P) and nodal ( V d) vertices. V a, V b and V c comprise the 3 classes of V d which connect 2, 1 and 0 V p respectively. The vertex ratio ( V R) of V a/ V b may be used to define topology since V a and V c approach equality in large networks. The introduction of trichotomous nodes ( V t, comprising V a′, V b′, V c′ and V d′, connecting 3, 2, 1 and 0 V p confounds vertex analysis in as much as the values of V R must be recalculated to maintain the definition of topology. Each V t is equivalent to 2 V d. V a′, V c′ and V d′ may be unequivocally transformed into V a + V b; V b + V c; and 2 V c respectively. However, V b, potentially contains V a, V b and V c in proportions which must be arbitrarily set, since the mode of growth only determines the frequencies of V t and not their transformation into V d pairs. We have assumed that all possible pairs of transformed V b, are equally likely and, accordingly, V b, is equivalent to V a/3 + 4 V b/3 + V c/3. The values of V R for different modes of growth, featuring different frequencies of V t, may thus be obtained by computer growth simulation. The mode of growth of observed networks may thereby be ascertained from V R, providing all V t are detectable in the tree.
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