The rapid growth of Internet of Things (IoT) environments has led to significant security challenges due to their dispersed, resource-limited, and constantly evolving characteristics. This study introduces a hybrid intrusion detection model that combines combinatorial graph theory, algebraic frameworks, and lightweight cryptographic approaches to strengthen protection in clustered IoT systems. The network structure is represented through discrete graph models, while algebraic methods—such as elliptic curve operations over finite fields and group-oriented key generation—are applied to secure interactions between cluster heads and sensor nodes.