Fig. 3: Comparison between the empirical distributions of the different macroscopic properties and theoretical equilibrium distributions computed using the transition matrices.

In (a), this comparison is depicted for the edges abundances, both the averages and wave by wave, while in the rest of the panels we depict only averages. In (b.1)–(b.8), this comparison is depicted for the eight different degree distributions. In (c), we depict the comparison for the triangle abundances. Since there are 1924 unique triangles spanning eight orders of magnitude, we have chosen a slightly different representation for the comparison. For each triangle motif, we plot the theoretical equilibrium abundances on the x-axis and the empirical abundances on the y-axis. Thus, each point corresponds to a theoretical-empirical pair for each motif, and the closer a point lies to the y = x line, the better the match between the two. For visualisation purposes, we have also included four exemplary motifs corresponding to some of the depicted points, chosen arbitrarily. In all cases, the error bars correspond to the 95% confidence intervals, and details for their computation are provided in the “Methods” section.