  Using the signed laplacian matrix, and weighted and hybrid graphs, we present
additional ways to interpret graphs as grid states. Hybrid graphs offer the
most general interpretation. Existing graphical methods that characterize
entanglement properties of grid states are adapted to these interpretations.
These additional classes of grid states are shown to exhibit rich entanglement
properties, including bound entanglement. Further, we introduce graphical
techniques to construct bound entangled states in a modular fashion. We also
extend the grid states model to hypergraphs. Our work, on one hand, opens up
possibilities for constructing additional families of mixed quantum states in
the grid state model. On the other hand, it can serve as an instrument for
investigating entanglement problems from a graph theory perspective.
