Table 2.

The numbers ${\mathcal{L}}_k(N)$ of simple connected pairwise nonisomorphic k-regular graphs on N vertices with degree $k\le 6$ used in this study, see e.g. Meringer (1999) and WolframMathWorld (2021)

N	k
	3	4	5	6
11	0	265	0	266
12	85	1.544	7.848	7.849
13	0	10.778	0	367.860
14	509	88.168	3.459.383	21.609.300
15	0	805.491
16	4.060	8.037.418
18	41.301
20	510.489
22	7.319.447

The numbers ${\mathcal{L}}_k(N)$ corresponds to the number of regular interaction networks with N individuals and k interacting neighbors for $11\le N\le 22$