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The $k$-ME concurrence as a measure of multipartite entanglement (ME)unambiguously detects all $k$-nonseparable states in arbitrary dimensions, andsatisfies many important properties of an entanglement measure. Negativity is asimple computable bipartite entanglement measure. Invariant and tangle areuseful tools to study the properties of the quantum states. In this paper wemainly investigate the internal relations among the $k$-ME concurrence,negativity, polynomial invariants, and tangle. Strong links between $k$-MEconcurrence and negativity as well as between $k$-ME concurrence and polynomialinvariants are derived. We obtain the quantitative relation between $k$-ME($k$=$n$) concurrence and negativity for all $n$-qubit states, give a exactvalue of the $n$-ME concurrence for the mixture of $n$-qubit GHZ states andwhite 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 polynomialinvariants, while for $4$-qubit states the relations between $k$-ME concurrence(for $k$=2, 4) and negativity, and between $k$-ME concurrence and polynomialinvariants also exist. Our work provides clear quantitative connections between$k$-ME concurrence and negativity, and between $k$-ME concurrence andpolynomial invariants.

Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle