Modern distributed systems and networks, like those found in cyber-physical system domains such as critical infrastructures, contain many complex interactions among their constituent software and/or hardware components. Despite extensive testing of individual components, security vulnerabilities resulting from unintended and unforeseen component interactions (so-called implicit interactions) often remain undetected. This paper presents a method for identifying the existence of implicit interactions in designs of distributed cyber-physical systems using the algebraic modeling framework known as Communicating Concurrent Kleene Algebra (C²KA). Experimental results verifying the applicability of C²KA for identifying dependencies in system designs that would otherwise be very hard to find are also presented. More broadly, this research aims to advance the specification, design, and implementation of distributed cyber-physical systems with improved cybersecurity assurance by providing a new way of thinking about the problem of implicit interactions through the application of formal methods.