Rapid urbanization has posed challenges to accessibility to critical services that require in-depth analysis. Complex networks theory has been used to evaluate the evolution of network topologies or the overall accessibility of transportation systems. However, topological metrics to explain the temporal changes in accessibility levels do not fully capture the dynamics and implications of accessibility to specific critical services. In this study, we address this gap and investigate the opportunities of using a self-avoiding random walk (SARW) algorithm to evaluate and explain the evolution of spatial accessibility to education facilities. We used hotspot analysis to understand the temporal changes and investigated changes in hot and cold spots over time. Furthermore, we explored the relationship between the network indicators and the SARW-based accessibility metric. We illustrated this method in a case study from Helsinki, where large-scale open data spanning from 1991 to 2016 is available. Our findings indicate that the SARW-based metric delivers more detailed node-level results than the traditional isochrone-based metric. The latter generates accessibility zones where accessibility is assumed to be uniform, while the SARW metric captures the dynamic nature of educational facility accessibility more accurately. The developed methodology helps to identify the impacts on the historical development of accessibility and can be applied to investigate accessibility to other critical services.@en