Algebraic topology methods in network security
D. Ganeshdganesh@outlook.comDepartment of Computer Science and EngineeringVardhaman College of EngineeringHyderabad, Telangana, 501218, IndiaView full profile → , M. Sudharsansudharsan.m@presidencyuniversity.inPresidency School of Information SciencePresidency UniversityBengaluru, Karnataka, 560119, IndiaView full profile → , I. Katharajkantharaj@jainuniversity.ac.inDepartment of Mechanical EngineeringFaculty of Engineering and TechnologyJAIN (Deemed-to-be University)Bangalore, Karnataka, 562112, IndiaView full profile → , *Samir N. AjaniCorresponding authorsamir.ajani@gmail.comSchool of Computer Science and EngineeringRamdeobaba University (RBU)Nagpur, Maharashtra, 440013, IndiaView full profile → , Saksham Soodsaksham.sood.orp@chitkara.edu.inCentre of Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140417, IndiaView full profile → , Rupesh Mishradrrupesh.mishra@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 27 Oct 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2821
- Pages:
- 3083–3095
Abstract
Attack surfaces are becoming dynamic, communications are increasingly encrypted and coordinated attacks are growing in complexity, creating more challenges for modern network security; traditional graph-based security solutions struggle to see the big picture and understand relationships among entities in the network. To secure the network an effective intrusion detection system, the authors propose a new model for Network Security–Persistent Homology-Based Network Security Model (PHNSM) which combines simplicial complex construction with homology computation, persistent homology, topological feature extraction, and graph neural networks-based threat classification. The proposed model is a multidimensional communication pattern, which is represented algebraically to be used for the effective identification of stealthy and distributed cyber-attacks in the global network, while maintaining the entire network function. Experimental evaluation is able to attain detection accuracy of 94.67%, precision of 94.18%, recall of 93.86%, F1-score of 94.02% and ROC-AUC of 96.08% and a 18.3% reduction in false-positive rate when compared to conventional graph-based security methods. The novelty is that the integration of persistent homology and deep topological learning for a cyber threat analysis with interpretation. The proposed framework provides mathematically sound, scalable and robust approach to anomaly detection, localization of attacks and large scale communication networks.
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References
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