Fig. 2: Network prediction limit vs. shortest compression length on empirical networks.
From: Revealing the predictability of intrinsic structure in complex networks
a For empirical networks drawn from different fields, the values \(({L}^{* },{H}_{{\rm{BPAA}}}^{* })\) fall on the linear relationship in the black straight line given by Eq. (3). The horizontal error bars indicate the standard derivation of the compression length across 50 calculations (see Supplementary Note 2). The standard deviation of the slope is 0.06 obtained by the bootstrap method34 and the coefficient of determination R2 is 0.93. b Similar plot to (a), with each empirical network having its links shuffled different number of times up to all of original links. After shuffling, the values \(({L}^{* },{H}_{{\rm{BPAA}}}^{* })\) move towards the point of ER network but still fall on the same linear straight line as in a. c Random addition of links up to the same number of links of the original network and (d) random removal of links up to half of original number of links in the various empirical networks. The resulting compression length L* and predictability \({H}_{{\rm{BPAA}}}^{* }\) still have the same linear relationship as the original networks in a A. e A schematic representation of combing two networks with the same nodes into one. f Values of LA+B vs. LA + LB in the case of shuffling links in empirical networks. A network after shuffling operation can be viewed as consisting of two independent subnetworks A and B: A refers to a network which only contains the shuffled links, i.e., an exact ER network; and the B is the remaining network with original links in the empirical network. g Similar plot to (f) in the case of randomly adding links in empirical networks. Here network A is an ER network containing all of the randomly added links while network B refers to the original real network.
