A bigram or digram is every sequence of two adjacent elements in a string of tokens, which are typically letters, syllables, or words; they are n-grams for n=2. The frequency distribution of bigrams in a string are commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, speech recognition, and so on.
Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar).
Head word bigrams are gappy bigrams with an explicit dependency relationship.
Bigrams help provide the conditional probability of a token given the preceding token, when the relation of the conditional probability is applied:
That is, the probability of a token given the preceding token is equal to the probability of their bigram, or the co-occurrence of the two tokens , divided by the probability of the preceding token.
Bigram frequency is one approach to statistical language identification.
Bigram Frequency in the English language 
The frequency of the most common letter bigrams in a small English corpus is:
th 1.52 en 0.55 ng 0.18 he 1.28 ed 0.53 of 0.16 in 0.94 to 0.52 al 0.09 er 0.94 it 0.50 de 0.09 an 0.82 ou 0.50 se 0.08 re 0.68 ea 0.47 le 0.08 nd 0.63 hi 0.46 sa 0.06 at 0.59 is 0.46 si 0.05 on 0.57 or 0.43 ar 0.04 nt 0.56 ti 0.34 ve 0.04 ha 0.56 as 0.33 ra 0.04 es 0.56 te 0.27 ld 0.02 st 0.55 et 0.19 ur 0.02
Complete bigram frequencies for a larger corpus are available.
See also 
- Michael Collins. A new statistical parser based on bigram lexical dependencies. In Proceedings of the 34th Annual Meeting of the Association of Computational Linguistics, Santa Cruz, CA. 1996. pp.184-191.
- Cornell Math Explorer's Project – Substitution Ciphers
- Jones, Michael N; D J K Mewhort (2004-08). "Case-sensitive letter and bigram frequency counts from large-scale English corpora". Behavior Research Methods, Instruments, & Computers: A Journal of the Psychonomic Society, Inc 36 (3): 388–396. ISSN 0743-3808. PMID 15641428.