  In social network, a person located at the periphery region (marginal node)
is likely to be treated unfairly when compared with the persons at the center.
While existing fairness works on graphs mainly focus on protecting sensitive
attributes (e.g., age and gender), the fairness incurred by the graph structure
should also be given attention. On the other hand, the information aggregation
mechanism of graph neural networks amplifies such structure unfairness, as
marginal nodes are often far away from other nodes. In this paper, we focus on
novel fairness incurred by the graph structure on graph neural networks, named
\emph{structure fairness}. Specifically, we first analyzed multiple graphs and
observed that marginal nodes in graphs have a worse performance of downstream
tasks than others in graph neural networks. Motivated by the observation, we
propose \textbf{S}tructural \textbf{Fair} \textbf{G}raph \textbf{N}eural
\textbf{N}etwork (SFairGNN), which combines neighborhood expansion based
structure debiasing with hop-aware attentive information aggregation to achieve
structure fairness. Our experiments show \SFairGNN can significantly improve
structure fairness while maintaining overall performance in the downstream
tasks.
