It has been known that, among pure states, N-qubit W states cannot be uniquely determined by their arbitrary (N - 1) bipartite reduced density matrices. Parashar and Rana proved that among arbitrary states, (N - 1) bipartite reduced density matrices that the pairs of qubits constitute a star graph or a line graph can uniquely determine stochastic local operations and classical communication (SLOCC) equivalent W states, and we generalize this conclusion into tree graph. In this paper, we show tha
