  Fair graph partition of social networks is a crucial step toward ensuring
fair and non-discriminatory treatments in unsupervised user analysis. Current
fair partition methods typically consider node balance, a notion pursuing a
proportionally balanced number of nodes from all demographic groups, but ignore
the bias induced by imbalanced edges in each cluster. To address this gap, we
propose a notion edge balance to measure the proportion of edges connecting
different demographic groups in clusters. We analyze the relations between node
balance and edge balance, then with line graph transformations, we propose a
co-embedding framework to learn dual node and edge fairness-aware
representations for graph partition. We validate our framework through several
social network datasets and observe balanced partition in terms of both nodes
and edges along with good utility. Moreover, we demonstrate our fair partition
can be used as pseudo labels to facilitate graph neural networks to behave
fairly in node classification and link prediction tasks.
