A Network Theory Approach to Assessing Environmental Sustainability in the Cruz Grande Region, Guerrero, Mexico

Traditional composite indicators for the study of sustainability often obscure the complex network of relationships among individual indicators, functioning as black boxes that fail to diagnose the underlying structural and functional weaknesses of the system. The objective of this research is to develop and apply a complementary approach grounded in network theory to diagnose and evaluate the structural and functional cohesion of environmental indicator systems. We developed a study that combines the Principal Component Analysis (PCA) method with network theory to comprehensively analyze the indicator system. The core of this contribution is the development of the $Mo\left(G\right)$ index, designed to quantify the structural–functional cohesion of an indicator network. This approach is applied to an environmental dataset of 19 indicators for Cruz Grande, Guerrero, Mexico (2010–2023). The results reveal that although the indicator network is relatively dense ($d=0.6199$), its structural–functional cohesion is low ($Mo\left(G\right)=520.68$), placing the region in the Fair category. This result provides an explanation for the sustained decline of the system, as shown by the PCA-based Regional Environmental Sustainability Index . We conclude that this approach is a complementary tool for diagnosing and evaluating environmental systems, enabling the detection of vulnerabilities that remain invisible to conventional aggregation methods.