  Real-world graphs are typically complex, exhibiting heterogeneity in the
global structure, as well as strong heterophily within local neighborhoods.
While a growing body of literature has revealed the limitations of common graph
neural networks (GNNs) in handling homogeneous graphs with heterophily, little
work has been conducted on investigating the heterophily properties in the
context of heterogeneous graphs. To bridge this research gap, we identify the
heterophily in heterogeneous graphs using metapaths and propose two practical
metrics to quantitatively describe the levels of heterophily. Through in-depth
investigations on several real-world heterogeneous graphs exhibiting varying
levels of heterophily, we have observed that heterogeneous graph neural
networks (HGNNs), which inherit many mechanisms from GNNs designed for
homogeneous graphs, fail to generalize to heterogeneous graphs with heterophily
or low level of homophily. To address the challenge, we present Hetero$^2$Net,
a heterophily-aware HGNN that incorporates both masked metapath prediction and
masked label prediction tasks to effectively and flexibly handle both
homophilic and heterophilic heterogeneous graphs. We evaluate the performance
of Hetero$^2$Net on five real-world heterogeneous graph benchmarks with varying
levels of heterophily. The results demonstrate that Hetero$^2$Net outperforms
strong baselines in the semi-supervised node classification task, providing
valuable insights into effectively handling more complex heterogeneous graphs.
