Inside the Voynich Network: graph analysis

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To go further into the Voynich graph analysis, I created a directed graph where every Voynich "word" is a node and each link connects words that appear next to each other inside the same paragraph. I avoided to connect words from one paragraph to the next one.Then I looked at how this network behaves.

Several things were found. There's not so much new, but a new apporach that gives the same rsults.

• A small group of words (like ol, chedy, shedy, qokain, aiin) form the backbone of the text. They connect to many others and often appear in short loops.
  
• The network isn’t random. When I shuffle the connections, most of the structure disappears.
  
• The text seems to remember what came before. Each word depends not only on the previous one but also on the last two or three. In other words, it has short-range grammar or a sort of rhythm rather than fixed phrases.
  
• There are no clear long repeating cycles. Instead, the same combinations keep reappearing in slightly different orders. Some words appear again after a short cycle, as shown in this plot:
      It shows that a few words, like chedy, qokeedy, shedy, daiin, tend to come back to themselves after two or three steps, while most others quickly lose that connection.
  

With this analysis, we can say the Voynich text behaves like a system that keeps recycling a few basic pieces under certain rules, not like plain gibberish.

According to the results, the next word is not random. it depends on the previous two or three words. This means the text follows a kind of rhythm or local grammar rather than fixed repeated phrases.
I tested it in three ways:

1. Conditional entropy drops sharply when more context is known.
   
2. Perplexity (remember it is the exponential of mean word entropy) decreases from 1-gram to 3-gram models.
   
3. Return probability in the token network is much higher than in random graphs.
   

Together these results suggest that Voynich writing behaves like a controlled system with short-range structure, not random typing. Here is the table summarizing the findings:

   

An additional plot to show the strongest repeating word transitions in the Voynich text, where a few tokens like ol, shedy, and qokedy form the main loop of tightly connected words: