What is graph signal processing and its applications?

Graph signal processing extends DSP to signals on irregular graph structures. Graph signal: Values on nodes, graph encodes relationships. Graph Fourier Transform: Eigendecomposition of graph Laplacian defines frequency, Graph Laplacian eigenvectors are basis functions. Graph filtering: Multiplication in graph spectral domain. Applications: Social network analysis, sensor networks (irregular placement), brain connectivity, point cloud processing, and recommendation systems. Challenges: Non-uniform sampling on graphs, computational complexity of large graphs, and graph uncertainty. Active research area extending classical DSP concepts to networked and irregular data structures.