  We prove that the squared R\'{e}nyi-$\alpha$ entanglement (SR$\alpha$E),
which is the generalization of entanglement of formation (EOF), obeys a general
monogamy inequality in an arbitrary $N$-qubit mixed state. Furthermore, for a
class of R\'{e}nyi-$\alpha$ entanglement, we prove that the monogamy relations
of the SR$\alpha$E have a hierarchical structure when the $N$-qubit system is
divided into $k$ parties. As a byproduct, the analytical relation between the
R\'{e}nyi-$\alpha$ entanglement and the squared concurrence is derived for
bipartite $2\otimes d$ systems. Based on the monogamy properties of
SR$\alpha$E, we can construct the corresponding multipartite entanglement
indicators which still work well even when the indicators based on the squared
concurrence and EOF lose their efficacy. In addition, the monogamy property of
the $\mu$-th power of R\'{e}nyi-$\alpha$ entanglement is analyzed.
