World Library  
Flag as Inappropriate
Email this Article


A trigram may also refer to Ba gua, a philosophical concept in ancient China. It may also refer to a three-letter acronym.

Trigrams are a special case of the n-gram, where n is 3. They are often used in natural language processing for doing statistical analysis of texts.


A typical cryptanalytic frequency analysis finds that the 16 most common character-level trigrams in English are:[1]

Rank Trigram
1 the
2 and
3 tha
4 ent
5 ing
6 ion
7 tio
8 for
9 nde
10 has
11 nce
12 edt
13 tis
14 oft
15 sth
16 men

Because encrypted messages sent by telegraph often omit punctuation and spaces, cryptographic frequency analysis of such messages includes trigrams that straddle word boundaries. This causes trigrams such as "edt" to occur frequently, even though it may never occur in any one word of those messages.


The sentence "the quick red fox jumps over the lazy brown dog" has the following word level trigrams:

the quick red
quick red fox
red fox jumps
fox jumps over
jumps over the
over the lazy
the lazy brown
lazy brown dog

And the word-level trigram "the quick red" has the following character-level trigrams (where an underscore "_" marks a space):

the he_ e_q
_qu qui uic
ick ck_ k_r
_re red


  1. ^ Lewand, Robert (2000). Cryptological Mathematics.   Table also available from
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.