Fig. 1: Network compression and BPAA performance entropy.

a Illustration of compression on network structural information. The lossless compression algorithm converts the network structure into a binary string, without retaining the labels of the nodes, and then compress the bit string to achieve the shortest compression length. b The shortest compression length of the shuffled networks. Here the shuffling operation is that we randomly pick f fraction of links from the original network and rewire them randomly. The compression length increases monotonically with f until f = 1, when the network becomes ER network. c Distribution of r_i of Metabolic network²⁹. Here we use RA algorithm³⁰ to do the prediction and each bar has the width equal to the network size N. The entropy of this distribution is representing the overall predictability. d The BPAA performance entropy H_BPAA vs. the link shuffling fraction f. We can see a monotonic trend similar to (b) is present for all of the three networks. Each line is the average of 50 simulations and the shaded region denotes the standard deviation. (Inset) Distribution of r_i of ER network with the same number of nodes and links as Metabolic network. The value of p_j is the average of 50 simulations.