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

General monogamy relation of multi-qubit systems in terms of squared R\'{e}nyi-$\alpha$ entanglement