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Fig. 5 | Applied Network Science

Fig. 5

From: Computational intractability law molds the topology of biological networks

Fig. 5

Effective instance size (EIS). a left pie charts: fraction of nodes in NEP instances having a certain benefit:damage (b:d) ratio (bottom legend) in the Fly PPI network and its synthetic analogs. The subset of nodes that need to be optimized over (those in all but 100:0, 0:100 slices) is significantly smaller in leaf-rich PPI (Fly) instances. Virtually all nodes in leaf-deprived NL network are ambiguous (0% nodes under 100:0 or 0:100 b:d ratios); right bar charts: break down of genes contributing to each b:d ratio slice in the corresponding pie chart, broken by gene degree (bottom legend); leaves dominate 100:0 and 0:100 slices in PPI. Because all nodes in NH network have degrees ≤4, no b:d ratio of any gene can fall in the 90:10/10:90 or 80:20/20:80 slices. b EIS for all networks; bar height represents the ambiguous pie slices in (a); each bar group corresponds to a MIN along with its corresponding NH, NL and RN analogs. In all networks, EIS is significantly smaller in real MINs compared to synthetic analogs. RN networks have more leaves (by sheer random re-assignment of edges in their creation) and therefore have smaller EIS compared to NL and NH

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