Diffusion of tacit knowledge in a company: a mathematical model based on diffusion on graphs

Purpose This paper aims to develop a novel mathematical model for identifying and diffusing tacit knowledge within organizations, particularly in the construction industry. It addresses the challenge of transforming personal, intangible assets into organizational drivers for innovation and competitive advantage. Design/methodology/approach The research uses graph theory and an analogy to the heat diffusion (Fourier’s Law) from physics to model knowledge transfer. It uses “Tacit Knowledge Transfer Graphs” (TKTG) and its adjacency matrix derived from employee questionnaires to quantify knowledge demand and the propensity to share. Jordan decomposition of the TKTG adjacency matrix is applied to identify optimal learning groups and dynamics. Findings The model effectively identifies “sources” and “sinks” of knowledge through eigenvector centrality. Analysis proves that organizing sessions based on TKTG leads to “equalizing” knowledge deficiencies among employees. Furthermore, Monte Carlo simulations suggest that lower knowledge demands allow for more flexible scheduling. Research limitations/implications Empirical validation remains outside the current scope. Future research will focus on organization-specific implementations and refining “knowledge conductivity” coefficients. Practical implications The model assists managers in optimal class scheduling, enhancing operational efficiency and reducing risks associated with losing critical knowledge keepers. Social implications By addressing unidentified knowledge demands, the model can improve organizational culture, support staff self-development and mitigate “quiet quitting” or high turnover. Originality/value This paper provides a unique mathematical formalization of tacit knowledge as an emergent process rather than a static object, offering a structured tool for knowledge management where descriptive methods previously dominated.