# Also in the Article

Scale free networks

Constructing graphs from genetic encodings
Sci Rep, Jun 24, 2021;

Procedure

We can summarize the scale-free heuristic from the main text, which generated networks with $pin=pout∼k-1$, using the pseudocode:

Here “connect” introduces the rule $(S)O(D)$ into the network. For instance, for b = 4 we connect 0000 to XXXX, 000X to XXX0, 00XX to XX00, 0XXX to X000, and XXXX to 0000 (Fig. (Fig.2,2, Main Text). The above code creates a directed network with nodes having equal out- and in-degree, while replacing a ‘0’ with a ‘1’ either in the S or D variable results in a network with separate in-hubs and out-hubs.

Through slight modifications of the heuristic, we can produce scale free networks with alternative $γ$. For instance, we can use b/2 rules, where we construct D sets as before, but add two Xs to each S set per iteration, resulting in $pin∼k-2$ and $pout∼k-0.5$ (Fig. S2):

In the case of b = 6, this would produce the rules $(000000)O(XXXXXX)$, $(0000XX)O(XXXXX0)$, $(00XXXX)O(XXXX00)$, and $(XXXXXX)O(XXX000)$.

Alternatively, we can use b/3 rules, where we construct D sets as before, but add three Xs to each S set per iteration, resulting in $pin∼k-3$ and $pout∼k-1/3$ (Fig. S3):

In the case of b = 6, this would produce the rules $(000000)O(XXXXXX)$, $(000XXX)O(XXXXX0)$, and $(XXXXXX)O(XXXX00)$.

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