  Network embedding, which maps graphs to distributed representations, is a
unified framework for various graph inference tasks. According to the topology
properties (e.g., structural roles and community memberships of nodes) to be
preserved, it can be categorized into the identity and position embedding.
However, existing methods can only capture one type of property. Some
approaches can support the inductive inference that generalizes the embedding
model to new nodes or graphs but relies on the availability of attributes. Due
to the complicated correlations between topology and attributes, it is unclear
for some inductive methods which type of property they can capture. In this
study, we explore a unified framework for the joint inductive inference of
identity and position embeddings without attributes. An inductive random walk
embedding (IRWE) method is proposed, which combines multiple attention units to
handle the random walk on graph topology and simultaneously derives identity
and position embeddings that are jointly optimized. In particular, we
demonstrate that some random walk statistics can be informative features to
characterize node identities and positions while supporting the inductive
embedding inference. Experiments validate the superior performance of IRWE
beyond various baselines for the transductive and inductive inference of
identity and position embeddings.
