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Inside the Voynich Network: graph analysis

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  • Inside the Voynich Network: graph analysis
• Inside the Voynich Network: graph analysis

• RE: Inside the Voynich Network: graph analysis

  Jorge_Stolfi > 28-10-2025, 08:16 PM

  (28-10-2025, 05:15 PM)Mauro Wrote: You are not allowed to view links. Register or Login to view.The same graph also brings me to re-evaluate Torsten Timm's work, because it's undeniable it's plotted 'near' the VMS, while its shuffled version is far away.

  
  The T&T generator is vaguely similar to a high-order word-based Markov model, so it naturally mimics the long-range correlations (up to 4 words apart and more) of the target language.  An English-based version of the T&T output (or of an order-3 Markov) should plot close to real English too, while their shuffled versions would plot far from it.

• RE: Inside the Voynich Network: graph analysis

  quimqu > 28-10-2025, 08:35 PM

  Mauro, thank you for the compliments.
  
  You got it right, the co-ocurrence graph has been created with a window of 5 tokens.
  
  Now I have some more tests to carry on:
  
  - see the differences with different windows
  - create the graph taking into account the paragraphs. I think this is important because my opinion is that the window of 5 should not take into account words from the next paragraph. This will reduce the edges and I am curious to see how different the graph KPI will be
  - I will post also graphs KPI for languages A and B
  
  Regarding the differences between texts of the same language, I think the graphs can help separating styles or themes of the texts. I will try to continue testing more texts.
  
  If anyone has any suggestion, I am open to try it through.

• RE: Inside the Voynich Network: graph analysis

  quimqu > 1 hour ago

  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.

• RE: Inside the Voynich Network: graph analysis

  quimqu > 1 hour ago

  I also repeated the Voynich run for K = 5, this time restricting co-occurrence windows to stay within paragraph boundaries, so that tokens at the end of one paragraph don’t link to those at the beginning of the next (note that in the previous results, the window could cath words from the next paragraph; in this run, I avoided this). The difference is subtle but measurable across several KPIs.
  
  

  Setting	Nodes	Edges	C	σ	Modularity	avg_degree	kcore_max	degree_gini	H_mean
  Voynich (K=5)	8744	130797	0.674	201.41	0.237	29.91	85	0.621	3.68
  Voynich (K=5, paragraph-limited)	8324	115394	0.712	219.29	0.228	27.73	82	0.651	4.28

  
  Confining the windows within paragraphs slightly reduces the network size and density, but the structure becomes more tightly clustered (C rises from 0.67 to 0.71) and even more small-world (σ ≈ 219 vs. 201). Restricting co-occurrences within paragraphs increases clustering while keeping path lengths comparable, which numerically raises σ. In practice, this means the network becomes more locally cohesive rather than globally more efficient. The degree distribution flattens a bit (higher Gini), and modularity remains stable. Mean entropy increases (which is expected, as limiting context makes each local neighbourhood less diverse, reducing the smoothing effect of cross-paragraph transitions).
  
  Limiting co-occurrences to within paragraphs makes the Voynich network smaller but more internally cohesive: words cluster more tightly inside paragraphs, paths stay short, and entropy rises as each section becomes more self-contained and less connected to the rest of the text.
  
  The overall picture suggests that paragraph boundaries act as real topological separators in the Voynich text. When preserved, they sharpen the internal cohesion of each component while still keeping the global small-world pattern intact, reinforcing the impression of a text with strong local repetition and high global connectivity.
  
  I am now re-running more text comparisons, even with language A and language B corpus (the Currier one's, not my topic modeling ones). I will try to post the results toorrow.
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