  This article delves into an analysis of the intrinsic entanglement and
separability feature in quantum states as depicted by graph Laplacian. We show
that the presence or absence of edges in the graph plays a pivotal role in
defining the entanglement or separability of these states. We propose a set of
criteria for ascertaining the separability of quantum states comprising
$n$-qubit within a composite Hilbert space, indicated as $H=H_1 \otimes H_2
\otimes \dots \otimes H_n$. This determination is achieved through a
combination of unitary operators, neighbourhood sets, and equivalence
relations.
