 For three variables formula_1, the interaction information formula_2 is given by

where, for example, formula_4 is the mutual information between variables formula_5 and formula_6, and formula_7 is the conditional mutual information between variables formula_5 and formula_6 given formula_10.Formally,

and

It thus follows that

For the three-variable case, the interaction information formula_2 is the difference between the information shared by formula_15 when formula_10 has been fixed and when formula_10 has not been fixed.