Context: Over the past decade, the adoption of Microservice Architecture (MSA) has led to the identification of various patterns and anti-patterns, such as Nano/Mega/Hub services. Detecting these anti-patterns often involves modeling the system as a Service Dependency Graph (SDG) and applying graph-theoretic approaches. Aim: While previous research has explored software metrics (SMs) such as size, complexity, and quality for assessing MSAs, the potential of graph-specific metrics like network centrality remains largely unexplored. This study investigates whether centrality metrics (CMs) can provide new insights into MSA quality and facilitate the detection of architectural anti-patterns, complementing or extending traditional SMs. Method: We analyzed 24 open-source MSA projects, reconstructing their architectures to study 53 microservices. We measured SMs and CMs for each microservice and tested their correlation to determine the relationship between these metric types. Results and Conclusion: Among 902 computed metric correlations, we found weak to moderate correlation in 282 cases. These findings suggest that centrality metrics offer a novel perspective for understanding MSA properties. Specifically, ratio-based centrality metrics show promise for detecting specific anti-patterns, while subgraph centrality needs further investigation for its applicability in architectural assessments.