  Graph Neural Networks (GNNs) have been broadly applied in many urban
applications upon formulating a city as an urban graph whose nodes are urban
objects like regions or points of interest. Recently, a few enhanced GNN
architectures have been developed to tackle heterophily graphs where connected
nodes are dissimilar. However, urban graphs usually can be observed to possess
a unique spatial heterophily property; that is, the dissimilarity of neighbors
at different spatial distances can exhibit great diversity. This property has
not been explored, while it often exists. To this end, in this paper, we
propose a metric, named Spatial Diversity Score, to quantitatively measure the
spatial heterophily and show how it can influence the performance of GNNs.
Indeed, our experimental investigation clearly shows that existing heterophilic
GNNs are still deficient in handling the urban graph with high spatial
diversity score. This, in turn, may degrade their effectiveness in urban
applications. Along this line, we propose a Spatial Heterophily Aware Graph
Neural Network (SHGNN), to tackle the spatial diversity of heterophily of urban
graphs. Based on the key observation that spatially close neighbors on the
urban graph present a more similar mode of difference to the central node, we
first design a rotation-scaling spatial aggregation module, whose core idea is
to properly group the spatially close neighbors and separately process each
group with less diversity inside. Then, a heterophily-sensitive spatial
interaction module is designed to adaptively capture the commonality and
diverse dissimilarity in different spatial groups. Extensive experiments on
three real-world urban datasets demonstrate the superiority of our SHGNN over
several its competitors.
