  In this paper, we introduce a category of one-parameter bipartite
entanglement quantifiers, termed $G_q$-concurrence ($q>1$), and show rigorously
that they satisfy all the axiomatic conditions of an entanglement measure and
can be considered as a generalization of concurrence. In addition, we establish
an analytic formula relating $G_q$-concurrence to concurrence for $1<q\leq2$ in
two-qubit systems. Furthermore, the polygamy relation is presented based on the
$G_q$-concurrence of assistance in multiqubit systems. As far as
$G_q$-concurrence ($1<q\leq2$) itself is concerned, however, it does not obey
the monogamy relation, but we prove that the square of $G_q$-concurrence does.
By means of this monogamy inequality, we construct a set of entanglement
indicators that can detect genuinely multiqubit entangled states even when the
tangle loses its efficacy.
