• 1. Introduction; 2. History and literature overview; 3. Calculus on undirected edge-weighted graphs; 4. Directed graphs; 5. The graph Ginzburg–Landau functional; 6. Spectrum of the graph Laplacians; 7. Gradient flow: Allen–Cahn; 8. Merriman–Bence–Osher scheme; 9. Graph curvature and mean curvature flow; 10. Freezing of Allen–Cahn, MBO, and mean curvature flow; 11. Multiclass extensions; 12. Laplacian learning and Poisson learning; 13. Conclusions; Bibliography.

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• 1. Introduction; 2. History and literature overview; 3. Calculus on undirected edge-weighted graphs; 4. Directed graphs; 5. The graph Ginzburg–Landau functional; 6. Spectrum of the graph Laplacians; 7. Gradient flow: Allen–Cahn; 8. Merriman–Bence–Osher scheme; 9. Graph curvature and mean curvature flow; 10. Freezing of Allen–Cahn, MBO, and mean curvature flow; 11. Multiclass extensions; 12. Laplacian learning and Poisson learning; 13. Conclusions; Bibliography.

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• 1. Introduction; 2. History and literature overview; 3. Calculus on undirected edge-weighted graphs; 4. Directed graphs; 5. The graph Ginzburg–Landau functional; 6. Spectrum of the graph Laplacians; 7. Gradient flow: Allen–Cahn; 8. Merriman–Bence–Osher scheme; 9. Graph curvature and mean curvature flow; 10. Freezing of Allen–Cahn, MBO, and mean curvature flow; 11. Multiclass extensions; 12. Laplacian learning and Poisson learning; 13. Conclusions; Bibliography.

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