Exponents of Growth - Systematic Design for Emergence in Cellular Nonlinear Networks - page 89

Fig. 5.17. Small world effects for gene ID = 801
5.5 On the Independence Between Various Measures
of Complexities
So far we introduced four measures of complexity (the transient length Trans , the
clustering coefficient Clus, the variance of the clustering coefficient Var , and the
exponent of growth U ). It is normal to ask whether these measures are independ-
ent or not. Ideally, a set of independent or orthogonal measures will be the best
choice. But we expect that a certain degree of dependence between these measures
exists.
Let us consider a CA family with a large number of members (“2s9” with
262,144 members) allowing the statistical characterization of the complexity
measures. Each complexity measure was calculated for all members of the family
giving a sequence (that may be associated with a random variable) with 262,144
samples. Figure 5.18 displays the direct functional relationship between all possible
pairs of complexity parameters.
These graphs reveal weak functional dependences between the four complexity
measures.