- Utilized `lanczos_iteration` to construct tridiagonal matrices, optimized for large, sparse matrices.
- Added `multiply_matrix_vector` for efficient matrix-vector multiplication using adjacency lists.
- Included `validate_adjacency_list` for input validation.
- Supports varied graph analysis applications, particularly for analyzing graph centrality.
- Included type hints, comprehensive docstrings, and doctests.
- PEP-8 compliant, with optimized handling of inputs and outputs.
This module provides essential tools for eigenvalue-based graph analysis, ideal for centrality insights and structural assessments.