  The $k$-ME concurrence as a measure of multipartite entanglement (ME)
unambiguously detects all $k$-nonseparable states in arbitrary dimensions, and
satisfies many important properties of an entanglement measure. Negativity is a
simple computable bipartite entanglement measure. Invariant and tangle are
useful tools to study the properties of the quantum states. In this paper we
mainly investigate the internal relations among the $k$-ME concurrence,
negativity, polynomial invariants, and tangle. Strong links between $k$-ME
concurrence and negativity as well as between $k$-ME concurrence and polynomial
invariants are derived. We obtain the quantitative relation between $k$-ME
($k$=$n$) concurrence and negativity for all $n$-qubit states, give a exact
value of the $n$-ME concurrence for the mixture of $n$-qubit GHZ states and
white noise, and derive an connection between $k$-ME concurrence and tangle for
$n$-qubit W state. Moreover, we find that for any $3$-qubit pure state the
$k$-ME concurrence ($k$=2, 3) is related to negativity, tangle and polynomial
invariants, while for $4$-qubit states the relations between $k$-ME concurrence
(for $k$=2, 4) and negativity, and between $k$-ME concurrence and polynomial
invariants also exist. Our work provides clear quantitative connections between
$k$-ME concurrence and negativity, and between $k$-ME concurrence and
polynomial invariants.
