Cloud microservice applications comprise interconnected services packed into containers. Such applications generate complex communication patterns among their microservices. Studying such patterns can support assuring various quality attributes, such as autoscaling for satisfying performance, availability and scalability, or targeted penetration testing for satisfying security and correctness. We study the structure of containerized microservice applications via providing the methodology and the results of a structural graphbased analysis of 103 Docker Compose deployment files from opensourced Github repositories. Our findings indicate the dominance of a power-law distribution of microservice interconnections. Further analysis highlights the suitability of the Barabási-Albert model for generating large random graphs that model the architecture of real microservice applications. The exhibited structures and their usage for engineering microservice applications are discussed.