Graph-based Modeling of Knowledge Flow Using Entropy, Markov Jump Processes, and Metropolis–Hastings

Effective knowledge management in organizations, universities, libraries, and research institutions requires optimizing the flow of information while accounting for uncertainty. We propose a probabilistic framework that models knowledge as a graph of facts, where each node represents a knowledge unit characterized by its entropy H(v), and edges indicate dependency or influence relationships. Transitions of information between nodes are represented as a Markov Jump Process (MJP), and transition probabilities are optimized using the Metropolis–Hastings algorithm to maximize knowledge flow. This framework identifies low-cost, high-impact pathways of knowledge transfer, enabling strategic decision-making in organizational learning and research. Simulation results demonstrate that maximizing mutual information between nodes reduces operational cost while promoting efficient knowledge dissemination.