A recent study reported that the construction management market has grown more competitive. In this environment, identifying a company's competitive position enables a study of competitor strategies and the ability to select the most suitable path to profitability. This study suggests a methodology to analyze topological competiveness based on social relationships between firms modeled according to four subnetworks: Joint contract networks linked directly between firms, public and private networks linked indirectly by owners, and building and civil networks linked indirectly by work type. This study proposes an analytical framework measuring topological competiveness from four perspectives: The network topology among each subnetwork, centralities and structural positions among the firms, cohesive subgroups and strong relations in the subnetwork, and the structural equivalence among firms. Using 2,984 cases of Korean construction management projects from 1997 to 2013, an empirical analysis of topological competiveness validated the methodology to diagnose competitiveness and select the most suitable relationships with competitors to create company growth.