Asian Journal of Pure and Applied Mathematics

Ecosystems are inherently complex, consisting of multiple interacting species, environmental factors, and anthropogenic influences. Understanding these interactions is crucial for predicting ecosystem stability, resilience, and responses to environmental changes. This paper explores the application of graph theory and computational modelling to analyse and quantify interactions within ecological networks. Graph theory provides a framework to represent species and their interactions as nodes and edges, enabling the identification of key species, trophic structures, and functional modules. Computational approaches, including network analysis algorithms, simulations, and modelling of dynamic processes, allow researchers to study the propagation of perturbations, the emergence of stability, and the impact of environmental stressors. Hybrid methods combining graph-theoretic metrics with probabilistic and stochastic models further enhance the prediction of ecosystem responses under uncertainty. Case studies demonstrate the effectiveness of these approaches in assessing food web stability, predicting species extinction cascades, and understanding spatial–temporal patterns of biodiversity. The paper also discusses challenges such as data incompleteness, uncertainty in interactions, and the computational complexity of large-scale networks. Future directions include integrating multi-layered networks, machine learning for pattern recognition, and real-time monitoring using sensor networks. Overall, the integration of graph theory with computational techniques provides a robust and versatile framework for ecosystem analysis, supporting conservation planning, sustainable resource management, and ecological risk assessment.