Urban areas are evolving in terms of their growing population and their developing systems and infrastructure. This evolution brings about concerns regarding social equity, which refers to the fairness of distribution of certain attributes to groups or individuals. Transport equity is one of the dimensions of this issue, and accessibility distribution is a commonly used indicator for its measurement. Such measurements are applied to urban transport systems to analyze the ease of accessing public services and areas of economic activity. With the development of complex network metrics and increased availability of historical data, temporal analysis of transport systems is gaining more attention. Complex network models based on graph-theoretical approaches provide a repeatable means for quantitative analysis of transport systems in terms of accessibility to opportunities. This research investigates the development of transport equity from the lens of spatial accessibility distribution over time and seeks to analyze its evolution using complex network theory. A random walk based accessibility methodology is developed for this purpose. This methodology is tested in a quantitative case-study, where the City of Helsinki is analyzed in terms of accessibility to education opportunities via walking as a travel mode. The results show that the developed methodology is useful for the identification of accessibility distribution, as well as equity evaluation. With the aid of topological network indicators, and spatial analysis of school locations, the effect of transport systems and land use can be distinguished. This method requires a complete data availability for each historical timestep, as well as adaptation of its parameters based on real-world travel behavior and infrastructural changes. Future research should investigate the multi-layer approach with the inclusion of other travel modes in the model. Furthermore, accessibility to other opportunities such as job locations can be tested with this methodology.