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Complex Analysis delves into the study of complex functions, which are those that have complex numbers as their inputs and outputs. It explores the properties and behavior of these functions, including concepts such as analyticity, singularities, and conformal mappings. In the context of Graph Theory under Mathematics within Science, Complex Analysis can be instrumental in analyzing networks with intricate structures and dynamics. For instance, it can provide insights into the distribution of eigenvalues in adjacency matrices of graphs or the behavior of electrical networks modeled as resistive circuits. Thus, Complex Analysis offers a powerful mathematical framework to investigate complex systems represented as graphs, thereby advancing our understanding of the underlying patterns and principles in these systems.