Safety-critical system domains such as critical infrastructures, aerospace, automotive, and industrial manufacturing and control are becoming increasingly dependent on the use of distributed systems to achieve their functionality. These distributed systems can contain many complex interactions among their constituent components. Despite extensive testing and verification of individual components, security vulnerabilities resulting from unintended and unforeseen component interactions (so-called implicit interactions) often remain undetected and can have an impact on the safety, security, and reliability of a system. This paper presents an approach for identifying and analyzing the existence and severity of implicit interactions in distributed systems. The approach is based on the modeling framework known as Communicating Concurrent Kleene Algebra (C²KA). Experimental results confirm that this approach can successfully identify and analyze dependencies in system designs that would otherwise be very hard to find. More broadly, the methods presented in this paper can help address the growing need for rigorous and practical methods and techniques for assuring the safe, secure, and reliable operation of distributed systems in critical domains.