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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. The Mathematical Association of America. p. 36. ISBN 978-0-88385-719-9.  Table also available from