digrams

A digram, also called a bigram in many applications, is a pair of adjacent elements in a sequence. Digrams can refer to any two consecutive units, such as letters, phonemes, or words. In statistical text analysis, digrams are the second-order units used to study the structure and patterns of a language.

In language analysis, two common forms are letter-level digrams and word-level digrams. Letter-level digrams are pairs of consecutive characters, for example in English the digrams “th,” “he,” “in,” and “er” frequently occur. Word-level digrams consist of consecutive words, such as “to be,” “in any,” or “the end.”

Applications of digrams span several fields. In natural language processing, digrams are foundational to n-gram models used for language modeling, text prediction, spelling correction, and auto-completion. In cryptography, digram frequency analysis examines how often pairs of letters occur to break ciphers and infer plaintext. Digrams also appear in data compression and authorship attribution, where patterns of adjacent items help distinguish texts.

Computation typically involves sliding a two-element window across the text, tallying occurrences of each digram, and optionally converting counts to probabilities, such as P(b|a) = count(ab) / count(a). For word-level digrams, tokens are generated for consecutive words, with appropriate preprocessing (case normalization, punctuation handling).

Limitations include data sparsity for longer or less common digrams, sensitivity to preprocessing choices, and dependence on corpus quality. Digrams capture local dependencies but not long-range structure, so they are often complemented by longer n-grams and smoothing techniques in practical applications.