Graph analysis approach was used to analyze a city bus network. The bus trip data were segregated into 4 smaller bus datasets (weekday-peak-hour, weekday-off-peak-hour, weekend-peak-hour, and weekend-off-peak-hour) with the main goal of studying and identifying the differences between peak hours and off-peak hours, as well as between weekdays and weekends. These differences are identified in terms of global characteristics and network evolution distinctions. Based on the analysis of the simplified network, we identified the relative shape of the networks and the centrality attributes. A comparative analysis is performed between the networks at different times to understand the impact of peak against off-peak and weekday against weekends. Significant differences are found in the analysis. In addition to the above, highly important routes and stops were also identified, where optimization initiative is planned for a more efficient bus transport network. The findings can serve as a starting point for future route optimization of the similar network. � Published under licence by IOP Publishing Ltd.