(a) Duplicate protein pairs lose their connectivity correlations over time. The average relative connectivity difference |k - k'|/(k + k') of duplicate pairs with connectivities k, k' > 0 is plotted against the time since duplication, parameterized by the synonymous (silent) nucleotide divergence K
. The horizontal line indicates the value expected for two randomly chosen nodes. The average number of duplicate pairs per bin was 16 (from low values of K
to high ones the number of duplicate pairs per bin were 12, 5, 3, 6, 6, 8, 13, 27, 44 respectively). (b) Duplications do not strongly influence network structure. The histogram shows the fraction of duplicate pairs among the k(k - 1)/2 neighbor pairs of a node of connectivity k plotted versus k. A high number of duplicate pairs would be expected if duplications were a significant mechanism of link gain, see text. The mean and the standard error of this fraction were determined using proteins which are products of duplicate genes with sequence similarity K
< 1. The number of vertices used per column ranges from 374 for k = 2 to 8 for k = 12.