The algebraic graph theory has a framework to study and construct secure communication systems based on a combination of structural graph properties, spectral graph properties and cryptographic concepts. This paper discusses attack modelling based on graphs with the actions of adversaries being modelled with respect to the edge between nodes, and the intrusion patterns can be formally defined. The spectral graph techniques are employed to detect anomalies that are determined by the eigenvalue distribution, laplacian matrices and connectivity to make it more accurate and robust. Further, algebraic structures, such as groups, rings and finite fields are also added to graph based cryptographic constructions to have a greater confidentiality and integrity. The proposed model is more robust in security where accuracy of intrusion detection is 28 percent better and a reduction in attack propagation is 22 percent, as compared to traditional ones. Results highlight the power, scalability and usability in dynamical network systems. The approach offers a unique, mathematical foundation of the design of secure communication, future developments of intelligent, graph driven cybersecurity systems.