Figure 1
Scaling in the distributions of branching ratio (degree) and sizes of the branches (subtrees). (a) Cumulative degree distributions for the ten largest trees. The dashed lines have slopes
and
indicating degree exponents
. In the whole data set, however, exponents
have been observed as well. (b) Cumulative distributions of branch size plotted as in (a). The dashed lines have slope
corresponding to branch size exponent
. The overall cumulative distribution of the sizes of the 16 452 branches in all 63 directory trees (thick solid curve) and the surrogate data from randomized trees (dot-dashed curve) are shown as well. (c) Allometric scaling: Each data point (small circle) shows cumulative branch size
(sum of sizes of all subbranches) against the size
of the branch itself. Logarithmic binning is applied to the original data (large circles) and the surrogate data from randomized trees (squares). The inset shows the binned original data rescaled with
(circles) and best fits for logarithm (solid line) and power law (dotted curve). The surrogate data in (b) and (c) are taken from 6300 trees, 100 trees obtained from each original tree by independent random rewiring. Rewiring is performed by iteratively swapping two randomly chosen node disjoint subtrees that do not contain the root. This standard network randomization procedure [
23], here applied to rooted trees, conserves the degree distribution.
Reuse & Permissions