  We show that the restricted sharability and distribution of multi-qubit
entanglement can be characterized by Tsallis-$q$ entropy. We first provide a
class of bipartite entanglement measures named Tsallis-$q$ entanglement, and
provide its analytic formula in two-qubit systems for $1 \leq q \leq 4$. For $2
\leq q \leq 3$, we show a monogamy inequality of multi-qubit entanglement in
terms of Tsallis-$q$ entanglement, and we also provide a polygamy inequality
using Tsallis-$q$ entropy for $1 \leq q \leq 2$ and $3 \leq q \leq 4$.
