Choosing a Graph

The foundational element for all operations in this library is the Graph Laplacian. It is a matrix that mathematically represents the structure and connectivity of your graph.

The Laplacian matrix L must be provided as a scipy.sparse.csc_matrix. This sparse format is essential for the high-performance memory and computation management provided by the underlying CHOLMOD library. The matrix must be square and symmetric.

Built-in Graph Repository

For convenience and reproducibility, sgwt includes a repository of pre-built graph Laplacians from common power system test cases. These can be imported directly.

The naming convention is METRIC_REGION. For a full list of available graphs and metrics, see the Laplacians section.

See also

• Laplacians for the complete list of built-in Laplacians.

• Graph Laplacian for the mathematical derivation and physical meaning of the weighting schemes.

import sgwt

# Load the Laplacian for the synthetic USA grid
# where edge weights are based on phase delay.
L_usa = sgwt.DELAY_USA

print(type(L_usa))
# Output: <class 'scipy.sparse.csc.csc_matrix'>

print(L_usa.shape)
# Output: (82223, 82223)