Inside the Voynich Network: graph analysis

[quimqu]

To compare the Voynich Manuscript with ordinary texts and Voynich languages A and B, I built word–co-occurrence graphs (window of 5 tokens) for each corpus (≈20,000 tokens each, except Voynich A ≈11,000 as it does not have more). I have detected that the metrics depend too much from the graph size (nodes) so I built this comparison with similar length texts.

For every graph I computed key network metrics: clustering ©, path length (L), small-worldness (σ), degree inequality (Gini), eigenvector concentration, and resilience under targeted attacks. As said, all texts were normalized in size to make the metrics comparable.

Here are the results:

Corpus	C	L	σ	Gini deg	Eigen conc.	Resilience ½
LA In Psalmum Exposito	0.63	2.48	4.40	0.55	0.0031	0.22
FR La reine Margot	0.69	2.26	3.03	0.62	0.0056	0.21
VOY Marco's Markov	0.65	2.46	3.19	0.62	0.0031	0.22
EN Romeo and Juliet	0.70	2.26	2.84	0.63	0.0053	0.23
DE Simpl. Simpl.	0.67	2.35	3.43	0.60	0.0039	0.21
Voynich EVA	0.66	2.60	3.95	0.58	0.0037	0.18
Voynich EVA A	0.65	2.56	4.18	0.53	0.0042	0.18
Voynich EVA B	0.67	2.58	3.60	0.59	0.0044	0.17
T.Timm	0.68	2.24	2.78	0.63	0.0069	0.24
CA Tirant lo Blanch	0.70	2.12	3.00	0.62	0.0085	0.22
Voynich CUVA	0.65	2.65	4.15	0.57	0.0033	0.18
LA De docta ignorantia	0.64	2.31	3.28	0.60	0.0063	0.26
ES Lazarillo	0.71	2.19	3.47	0.58	0.0079	0.19
Naibe Cipher	0.62	2.33	3.23	0.58	0.0040	0.29
VI Vietnamese Stolfi	0.67	2.16	2.20	0.62	0.0063	0.31

What we can see:

- All Voynich sections have higher σ (small-worldness) than ordinary texts, meaning stronger local clustering and weaker global connectivity (Note: in this calculation, the small-world coefficient σ was computed against degree-preserving random graphs, not simple Erdős–Rényi graphs. This means each random control graph keeps the same degree distribution as the original, making σ more reliable for linguistic networks. That's why the values are lower than in previous posts)
- Average path length L is slightly longer: information (or adjacency) travels less efficiently across the graph, suggesting that the network is more fragmented into local clusters with fewer bridging links connecting them.
- Degree Gini is lower: no strong “hub” tokens comparable to function words in real languages, indicating a more uniform connectivity pattern where all nodes share similar importance instead of a few dominating the network.
- Eigenvector concentration and resilience are both lower: influence and robustness are evenly spread rather than hierarchical, implying that the network lacks dominant central nodes and would fragment quickly if connections were removed.

I show here a couple of plots:

           

Natural languages form networks with a few highly connected function words and many peripheral ones.
The Voynich graphs are more uniform and modular: dense local clusters, few bridges, and a fragile large-scale structure.

As deduced throughout the thread, this pattern fits a system built from repetitive combinational rules rather than a natural linguistic process, with structural dependencies extending across at least five-token window rather than just immediate bigram links.