Graph models and operations in evaluating microservice solutions

Abstract

Microservice architecture played an important role as a dominant factor in different software system design, it offers scalability and the ability to maintenance. The increasing complexity of microservice-systems faces significant challenges in understanding and evaluation. This paper proposes a formal and mathematical representation of microservice architecture using graph theory, where each microservice is represented as a vertex and each communication or dependency between two microservices is represented as a directed edge. Mathematical model based on adjacency matrices was introduced, graph theory algorithms is explored. Graph metrics were studied to analyze structural properties, find critical nodes, and detect potential failure points. Other operations are also explored such as analysis of path, finding and detecting cycles, and connectivity evaluation, these operations are important for testing, reliability assessment, and fault tolerance in distributed systems. The proposed approach is tested on a case study of a hypothetical microservice system. The recommendations suggest that graph-theoretic modeling provides a powerful foundation for the formal analysis, monitoring, and optimization of microservice architectures. doi 10.54708/19926502_2026_30111165