Leveraging Nonassociative Algebra for Spectral Analysis of Anomalies in IoT

The constantly changing characteristics of distributed networks and Internet of Things and additionally their susceptibility to anomalies render maintaining security and resilience complicated. This research provides a spectral-based anomaly detection framework connected with nonassociative algebra, inverse property quasigroup. By investigating the adjacency and Laplacian spectra, we can recognize structural changes caused by improper access, node failures, and cyber threats. We introduce left and right inverse graphs linked to a specific category of finite quasigroups and demonstrate the relationship between algebraic structures and bipartite graphs via edge labeling. In this study, we analyze the inverse property quasigroup, commutator subloop, associator subloop, and nucleus, along with their corresponding directed and undirected graphs. Additionally, we provide findings on spectra, vertex connectivity, edge connectivity, and algebraic connectivity pertaining to these graphs and see their role in distributed networks and anomaly detection in Internet of Things.