Inter-city mobility is one of the most important issues in the UN Sustainable Development Goals, as it is essential to access the regional labour market, goods and services, and to constrain the spread of infectious diseases. Although the gravity model has been proved to be an effective model to describe mobility among settlements, knowledge is still insufficient in regions where dozens of megacities interact closely and over 100 million people reside. In addition, the existing knowledge is limited to overall population mobility, while the difference in inter-city travel with different purposes is unexplored on such a large geographic scale. We revisited the gravity laws of inter-city mobility using the 2.12 billion trip chains recorded by 40.48 million mobile phone users' trajectories in the Jing-Jin-Ji Region, which contains China's capital Beijing. Firstly, unlike previous studies, we found that non-commuting rather than commuting is the dominant type of inter-city mobility (89.3%). Non-commuting travellers have a travel distance 42.3% longer than commuting travellers. Secondly, we developed more accurate gravity models for the spatial distribution of inter-city commuting and non-commuting travel. We also found that inter-city mobility has a hierarchical structure, as the distribution of inter-city travel volume follows Zipf's law. In particular, the hierarchy of non-commuting travel volume among the cities is more in line with an ideal Zipf distribution than commuting travel. Our findings contribute to new knowledge on basic inter-city mobility laws, and they have significant applications for regional policies on human mobility.
