We employ statistical and graph theoretical methods to explore the relationship between structural topology and information content in two dimension carbon nitride \((C_{2}N)\) monolayers. To this end, we consider several degree-based Zagreb-type indices together with entropy measurement to investigate the inherent complexity and information encoding capacity of \((C_{2}N)\) network. The quantification of the entropy and topological indices provide molecular connectivity and system disorder data. Logarithmic regression modeling is employed to determine nonlinear relationships between entropy and indices, and is also justified using Pearson correlation analysis. The strong correlation coefficients found in this work support these indices as reliable metrics for assessing the structure and complexity of \((C_{2}N)\) materials, with potential applications in materials science and nanotechnology.
