Logic can be used to precisely express human thoughts and inferences. In this paper, an approach using first-order logic for knowledge representation of software component interconnection information to facilitate the validity and integrity checking of the interconnection among software components during software development or modification is presented. Directed graphs are first used to model the structure and behavior of a large-scale software system, and a first-order theory of directed graphs (the DG theory) is established. The interconnection behavior among software components in a large-scale software system is a directed graph which is called software component interconnection graph (CIG). The behavior of the CIG is interpreted using the DG theory and translated into logic representation. The translated logic representation is a set of logic clauses and can be considered as a set of axioms. Automated reasoning techniques based on these axioms can be used to perform the validity and integrity checking of software properties in the software development or maintenance phase.