This paper offers a novel method for modeling and assessing network resilience against cyber-attacks by utilizing discrete structures and algebraic techniques. Utilizing edge and node representations taken from actual intrusion detection datasets build a network graph and examine its structural aspects to identify attack trends and resilience traits. The selection of key characteristics via correlation analysis, supervised machine learning classifiers—Support Vector Machine (SVM), Random Forest (RF), and K-Nearest Neighbors (KNN)—are used to predict and categorize attack types. Confusion matrices and common classification metrics, accuracy, precision-, recall, and F1-score-0.99, are used to assess the models. This research supports SDG 9 by advancing secure and resilient infrastructure through innovative use of algebra and discrete structures. It also aligns with SDG 16 Peace Justice and strong institutions by contributing to the development of secure institutions.