Spectral Coarse-Graining Theory
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Spectral Coarse-Graining (SCG) reduces a complex network while preserving diffusion dynamics.

Given adjacency matrix :math:`A`, the normalized Laplacian is:

.. math::

   L = D^{-1/2}(D - A)D^{-1/2}

Key spectral properties:

- **Algebraic connectivity** :math:`\lambda_2`: network robustness
- **Spectral gap** :math:`\Delta = \lambda_{k+1} - \lambda_k`: cluster boundary
- **Spectral radius** :math:`\rho`: contagion speed

SCG risk score:

.. math::

   \text{SCG Risk} = 1 - \frac{\lambda_2}{\rho}

Ranges from 0 (robust) to 1 (fragile).