Using Viterbi algorithm to decrypt Vernam cipher

I'm reading a book on cryptography and it mentions the Viterbi algorithm being used to decrypt Vernam cipher if the same key is used multiple times.

According to the book the Viterbi algorithm takes a weighted directed graph whose edges are labelled by letters and the weights correspond to transition probabilities. Given a starting vertex and a word it returns the highest probability path starting from this vertex and such that the edges passed are labelled by the letters of the word in order.

I have three cipher texts that have been obtained by using the Vernam cipher with the same key.

I'm guessing the edges should represent the cipher text and the vertices should represent the clear text but I cannot figure it out.

• What is "it" in the final sentence / question? How to use the entire algorithm? Just a request for some clarification. Oct 31 '19 at 17:00
• I'm wondering what should the vertices / edges / weights be in the algorithm. For instance if the vertices represent the clear text letter, the weights could represent the letter frequencies of the language but then how do you label the edges ? Oct 31 '19 at 17:08