  We combinatorially characterize the number $\mathrm{cc}_2$ of conjugacy
classes of involutions in any Coxeter group in terms of higher rank odd graphs.
This notion naturally generalizes the concept of odd graphs, used previously to
count the number of conjugacy classes of reflections. We provide uniform bounds
and discuss some extremal cases, where the number $\mathrm{cc}_2$ is smallest
or largest possible. Moreover, we provide formulae for $\mathrm{cc}_2$ in free
and direct products as well as for some finite and affine types, besides
computing $\mathrm{cc}_2$ for all triangle groups, and all affine irreducible
Coxeter groups of rank up to eleven.
