Inside the Voynich Network: graph analysis

[quimqu]

I’ve run the co-occurrence graphs for window sizes from K = 1 up to 10 on the same four corpora: Alchemical Herbal Latin, Tirant lo Blanch, Torsten Timm’s generated text, and the Voynich Manuscript.
The global behaviour is smooth across all K, and most indicators move monotonically: clustering grows, path length shortens, modularity declines. Yet the Voynich keeps its peculiar position: extremely small-world at every scale, moderately modular, and lower in entropy.

Corpus	K	C	σ	Modularity	H_mean
AlchemicalHerbalLatin	1	0.550	86.67	0.424	2.41
	2	0.550	86.67	0.427	2.41
	3	0.620	60.86	0.373	2.94
	5	0.680	39.45	0.303	3.59
	7	0.707	29.47	0.259	4.01
	10	0.729	21.36	0.223	4.44
Tirant_lo_Blanch	1	0.637	169.75	0.235	2.79
	2	0.637	169.75	0.239	2.79
	3	0.680	119.96	0.196	3.30
	5	0.716	78.99	0.155	3.93
	7	0.729	59.49	0.136	4.33
	10	0.739	43.82	0.121	4.74
TorstenTimm	1	0.610	144.11	0.142	2.99
	2	0.610	144.11	0.142	2.99
	3	0.664	109.02	0.130	3.48
	5	0.706	76.33	0.113	4.09
	7	0.725	60.25	0.107	4.47
	10	0.739	46.54	0.103	4.87
Voynich	1	0.535	410.18	0.281	2.50
	2	0.535	410.18	0.284	2.50
	3	0.615	307.83	0.267	3.02
	5	0.674	201.41	0.237	3.68
	7	0.698	152.95	0.232	4.11
	10	0.717	115.74	0.223	4.56

Across all corpora, increasing K makes the graph more tightly connected and less modular, but the Voynich keeps its distinct profile. Its small-world index is several times larger than any other text at every scale, and even at K = 10 it remains roughly twice that of the closest competitor. Clustering converges around 0.7 for all, yet Voynich begins lower and catches up only slowly. Modularity drops from 0.28 to 0.22, remaining midway between the natural languages and the Timm generator. Entropy grows with K as expected, but the Voynich still shows lower H_mean and a higher proportion of deterministic transitions.

The K-sweep reinforces the pattern seen before: the Voynich network is not random, but its combination of high connectivity, modest modularity, and low entropy makes it stand apart from both natural language and algorithmic texts.