Structural coupling metrics for microservice architectures with dependency weighting

Context. Microservice architectures support modularity and independent deployment, but they also introduce complex inter-service dependency structures that may increase the risk of change propagation. Existing coupling metrics capture service connectivity, yet they often treat dependencies as binary or additive and provide limited information about dependency direction, internal structural reach, and the proportion of callee logic involved in an interaction. Objective. This paper aims to provide a more expressive static characterisation of structural coupling in object-oriented microservice systems. The goal is to provide implementation-aware indicators for analysing pairwise, incoming, and outgoing dependency patterns relevant to architectural maintainability assessment. Method. We introduce three metrics: Microservice Quality Measure (MQM) for pairwise coupling, afferent Microservice Quality Measure (aMQM) for incoming dependency intensity, and efferent Microservice Quality Measure (eMQM) for outgoing dependency intensity. The metrics are defined at the class level and capture two additional factors: the distance between internal classes and the proportion of callee logic used by callers. An exploratory evaluation was conducted on 15 open-source Java/Spring Boot microservice systems comprising 100 services. The proposed metrics were compared with established reference metrics using correlation analysis, principal component analysis, and discriminative-power assessment. Results. The proposed metrics showed strong correlations with established coupling measures, indicating consistency with existing structural coupling indicators. At the same time, the analysis suggests that MQM, aMQM, and eMQM provide complementary information about dependency structure by distinguishing service pairs and services with different internal structural profiles. Across the analysed systems, the proposed metrics achieved higher discriminative power than the selected baselines, indicating greater sensitivity to structural variation in the examined dataset. Conclusion. MQM, aMQM, and eMQM constitute complementary static indicators for analysing structural dependency patterns in object-oriented microservice architectures. They enrich architectural inspection by capturing aspects of coupling that are only partially reflected in existing measures. The resulting structural insights can support architectural inspection during maintenance and evolution activities.