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Fig. 6 | Applied Network Science

Fig. 6

From: Computational intractability law molds the topology of biological networks

Fig. 6

Search space size. The total search space (grey) of a given NEP instance is quantified as St=2O(n) where n is the number of genes in the instance with either benefit score b>0 or damage score d>0. Effective search space (blue) is defined as Se=2O(m) where \(m\leq n=\sum \limits _{i=1}^{n}{1-\delta _{i}}\) and \({\delta }_{i}=\frac {|b_{i}-d_{i}|}{b_{i}+d_{i}}\) is the ambiguity measure of gi under the current NEP instance (bi,di are the benefit,damage scores of gene gi). Networks are grouped by size for better y-axis readability. Note that the y-axis values are logarithmic in base 2, and hence linear differences between bar heights imply exponential differences in St or Se. Smaller but denser NL networks have smaller St relative to other networks but suffer from having extremely high Se: St ratio due to the high ambiguity of its nodes under NEP instances. Biological networks have exponentially smaller Se: St ratio relative to corresponding NL, NH, and RN random analogs by virtue their having a higher number of leave nodes, particularly genes of degree 1-3, which are more likely to be unambiguously beneficial or damaging under a given NEP instance, and as such have relatively higher δ values (= smaller m exponent overall)

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