This study uses a topological Markov chain model to establish a framework to evaluate the structural quality in a university library in Taiwan. With the transition matrix and the level of user satisfaction, the topological invariant can be computed to evaluate the structural quality given the different levels of user satisfaction. Some fundamental properties, such as reducibility, periodicity, connectedness, and stability, to analyze the structure of a topological Markov chain model for a transition matrix are provided. A framework is depicted, and a brief illustration of using a topological Markov chain model is discussed in this study.
