Laplacian Matrix

The Laplacian matrix is a mathematical tool used to analyze the structure of a network or graph. It captures how nodes (points) are connected and measures the difference between each node's value and the average of its neighbors. This helps identify important features like clusters or bottlenecks within the network. The matrix is constructed from the degree of each node (number of connections) and the connections themselves, making it useful in areas like data analysis, physics, and computer science to understand flow, connectivity, and the overall shape of complex systems.