The purpose of this research is to study the communication network among the participants in a construction project. The proposed approach contains the solving of the following tasks: identification of the key factors that affect the communication quality; calculation of the “communication quality” indicator between each pair of participants using fuzzy logic; and evaluation of the key measures of centrality using the tools of a Social Network Analysis. Solving the set tasks can help break the problem of the low level of efficiency of construction project deliveries. This study was conducted when the design stage was already complete and the construction project had 17 participants. We used the following factors influencing communication quality: timeliness, understanding, bidirectionality, use of IT tools in communication acts and adequacy. The use of fuzzy logic tools can minimise the subjectivity of the qualitative data obtained from the questionnaires. The analysis of five centrality measures showed that “Project manager”, “Chief engineer”, “Construction site manager”, “Construction works manager” and “Architect” had the greatest values in comparison with other network participants. On the one hand, this organisational structure of communication can be considered correct because the main information flows through the project managers, who make the decisions. On the other hand, this indicates a significant dependence of the construction project on these participants and, in the event of certain risk events, may lead to a decrease in the efficiency of its implementation. The methods presented in this article can be used in project management to analyse a real communication network.