GraphenLaplaceOperator
GraphenLaplaceOperator is a Laplacian-type operator defined on graphs, commonly used to model diffusion, vibrational modes, and quantum-like processes on discrete structures. In its standard form it acts on functions defined on the vertices of a graph and encodes the connectivity through edge weights.
For a simple undirected graph G with adjacency matrix A and degree matrix D (where D is
A normalized variant, often used in data analysis, is L_norm = I − D^−1/2 A D^−1/2, or equivalently
In the context of graphene, the GraphenLaplaceOperator is frequently applied to the honeycomb lattice, a bipartite
Applications include spectral clustering, graph signal processing, diffusion, and modeling of vibrational and electronic properties on