  In this paper we give a method to associate a graph with an arbitrary density
matrix referred to a standard orthonormal basis in the Hilbert space of a
finite dimensional quantum system. We study the related issues like
classification of pure and mixed states, Von-Neumann entropy, separability of
multipartite quantum states and quantum operations in terms of the graphs
associated with quantum states. In order to address the separability and
entanglement questions using graphs, we introduce a modified tensor product of
weighted graphs, and establish its algebraic properties. In particular, we show
that Werner's definition [1] of a separable state can be written in terms of a
graphs, for the states in a real or complex Hilbert space. We generalize the
separability criterion (degree criterion) due to S.L. Braunstein, S. Ghosh, T.
Mansour, S. Severini, R.C. Wilson [2], to a class of weighted graphs with real
weights. We have given some criteria for the Laplacian associated with a
weighted graph to be positive semidefinite.
