<p>This study establishes the foundational framework of the complex spherical fuzzy environment, which has emerged as a powerful tool for representing two dimensional ambiguous information with greater precision. The limitations of existing frameworks specifically, the inability of complex Pythagorean fuzzy sets to express abstention due to the absence of a neutral membership component, along with the restricted capacity of spherical fuzzy sets to represent two-dimensional information have motivated the development of the complex spherical fuzzy set (CSFS) theory. The CSFS framework is adapted to construct the complex spherical fuzzy graph structure (CSFGS), in which graph elements are assigned complex spherical fuzzy values to capture uncertainty within network models. This proposed theory introduces a novel balanced concept for CSFGS and establishes key properties such as average CSFGS and density. The constructed graph-based network is analyzed to determine whether its structure exhibits intense or feeble characteristics, offering deeper insights into the behavior of complex spherical fuzzy networks. This theory also examines key structural aspects of balanced CSFGS networks, including subdivision, isomorphism, identical forms, and their complements. In addition, novel operations such as the modular product and its related properties are investigated, providing a deeper understanding of the behavior and structure of balanced CSFGS. The proposed results are applied to identify the optimal demand distribution of renewable and non-renewable electricity generation in India. To support this analysis, novel CSFA and CSFWA operators are introduced and employed to evaluate alternative energy sources. An algorithm is developed to implement the proposed application, and the outcomes are compared and discussed to demonstrate the effectiveness and practicality of the CSFGS approach.</p>