Graphic Approximation of Integer Sequences

The chapter delves into the crucial area of modeling real-world complex networks using graph models. It focuses on the initial step of constructing graphs with given degree sequences, a problem that often involves dealing with non-graphic integer sequences. The authors present two innovative approaches to approximate these sequences: one that minimizes discrepancy using unit transformations within the majorization lattice, and another that minimizes the probability distribution distance. Both algorithms are designed to be efficient and easy to implement, requiring only linear memory. The chapter also introduces the concept of majorization and its relationship with graphic sequences, providing a solid foundation for understanding the algorithms. The research highlights the practical advantages of these methods, especially for large sequences, and suggests future directions for exploring other distance metrics like the Jensen-Shannon divergence.