  Inversive distance circle packing metric was introduced by P Bowers and K
Stephenson \cite{BS} as a generalization of Thurston's circle packing metric
\cite{T1}. They conjectured that the inversive distance circle packings are
rigid. For nonnegative inversive distance, Guo \cite{Guo} proved the
infinitesimal rigidity and then Luo \cite{L3} proved the global rigidity. In
this paper, based on an observation of Zhou \cite{Z}, we prove this conjecture
for inversive distance in $(-1, +\infty)$ by variational principles. We also
study the global rigidity of a combinatorial curvature introduced in
\cite{GJ4,GX4,GX6} with respect to the inversive distance circle packing
metrics where the inversive distance is in $(-1, +\infty)$.
