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 word given the preceding word, when Bayes' theorem is applied:
That is, the probability of a word given the preceding word is equal to the probability of their bigram, or the co-occurrence of the two words , divided by the probability of the preceding word.
TH 50 AT 25 ST 20
ER 40 EN 25 IO 18
ON 39 ES 25 LE 18
AN 38 OF 25 IS 17
RE 36 OR 25 OU 17
HE 33 NT 24 AR 16
IN 31 EA 22 AS 16
ED 30 TI 22 DE 16
ND 30 TO 22 RT 16
HA 26 IT 20 VE 16
However, these counts are different than other published results; one from the Cornell University Math Explorer's Project (measured over 40,000 words or about 200,000 letters) gives the first five as follows: