DIMENSION OF FIBONACCI NETWORK

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Modern complex network theory reveals that real-world systems possess not only small-world and scale-free topological features, but may also exhibit statistical self-similarity and fractal scaling. Within the framework of fractal geometry and iterated function systems, this paper investigates the geometric dimension of a class of networks generated from binary structures. Inspired by the Frostman measure theory, we adopt the definition of the Frostman dimension for a family of networks and systematically compute the dimension for networks derived from the full binary tree and from a restricted subtree where consecutive left-child nodes are forbidden. Through precise combinatorial analysis and asymptotic estimation, we prove that the Frostman dimension of the binary tree is [Formula: see text], while the dimension of Fibonacci network — whose node growth follows the Fibonacci sequence — is [Formula: see text], where [Formula: see text] is the golden ratio. The results show that the geometric dimension of such binary networks coincides with the fractal dimension of classical sets such as the Cantor set, and in the Fibonacci case, is closely related to the Fibonacci entropy. This establishes a deeper connection between network science and fractal geometry. The study provides new theoretical insights and computational methods for understanding the fractal properties of networks under regular and constrained growth mechanisms.