## 1 Introduction  
Since the end of the 20 th century, with the increasing development of globalisation and informatisation, the flow of various elements (people, goods, knowledge and information) has become more frequent across various scales, and accordingly, regions have become the space of flows [1]. In this context, the concept of space of flows is gradually replacing the space of place [2]. Mobilities have become a hallmark of modern times [3]. The emergence of flow space has had a disruptive impact on space-distance-based and cored geography [4]. Regional spatial morphology is also being redefined and modified as researchers from multiple disciplines have begun to recognize and analyse spatial structure using the flow rather than central place perspective [5]. As the most important form of spatial interaction to connect and increase communication between different geographical spaces, transport flow undoubtedly has remarkable impacts on economic activity space and is a key factor in the shaping of socio-economic spatial structure [6]. Understanding these impacts has wider significance for interpreting the spatial distribution law of various economic phenomena [7]. With the increasing demand for fast inter-city transport, the infrastructure including expressways, airlines, high-speed railways and ETC (Electronic Toll Collection) systems have become the most important parts of the modern transport system [8]. As such, the transport flows over the network of these infrastructure systems have been widely studied. The regional transport flow on well-networked expressways has contributed remarkably to the socio-economic links between large and medium cities [9], particularly in view of the spatial interactions [10]. Compared with the air and railway networks, the expressway network has its own unique characteristics. Firstly, the flow pattern is much more complex due to high frequency and dynamics, which results in spatial heterogeneity [8]. Secondly, the transport flow on such network is more fragile and vulnerable to many physical and human factors (e.g., weather, accidents and regulations), it can be envisioned that its spatial interaction patterns have strong economic and demographic effects and implications for policy-making [11]. Thirdly, such a pattern with the mixture of long- and short-distance flows across the region indicates varied levels of urban agglomeration [12]. In the field of geographical mobility, there is a long history of deploying a gravity model to analyse the spatial economic interactions between cities and regions by considering a variety of physical, social, economic and even environmental dimensions [13; 14]. The traditional methods of calibrating the spatial interaction models are dominated by global regression models (e.g., Ordinary Least Square (OLS), Poisson Regression and negative binomial regression) based on the assumption that the mobility pattern is spatially stationary. However, the socio-economic systems driving the transport flows at a regional scale demonstrate heterogeneous density, intensity and diversity. This has resulted in the development of flow models by considering spatial heterogeneity, which will be calibrated by local regression methods. There is a recent development of such local regression methods in geography in considering spatial non-stationarity, among which geographically weighted regression (GWR) has become one of most popular approaches [15]. The extension of GWR into flow modelling was initiated by the seminal paper of spatially weighted interaction models (SWIM) [16]. This modelling method was upgraded to geographically weighted negative binomial regression (GWNBR) [17]. In parallel, the flowAMOEBA method, based on a multidirectional optimum ecotope-based algorithm, is able to analyse flow patterns through defining a spatial flow neighborhood [18].