Developed and delivered Laplacian matrix computation for Cayley graphs in the cayleypy repository, enabling spectral analysis and expanded graph metrics within the library. The work involved designing and implementing an algorithm in Python that accurately computes the Laplacian for these specialized graphs, with a focus on correctness and extensibility. Comprehensive unit tests were created to validate the implementation, and related test issues were resolved to improve reliability. This contribution strengthens cayleypy’s graph theory capabilities and supports advanced analytics and research workflows. The project leveraged skills in algorithm development, graph theory, and unit testing to enhance the library’s analytical foundation.