  A hypergraph is a data structure composed of nodes and hyperedges, where each
hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge
size, hypergraphs represent group interactions (e.g., co-authorship by more
than two authors) more naturally and accurately than ordinary graphs.
Interestingly, many real-world systems modeled as hypergraphs contain
edge-dependent node labels, i.e., node labels that vary depending on
hyperedges. For example, on co-authorship datasets, the same author (i.e., a
node) can be the primary author in a paper (i.e., a hyperedge) but the
corresponding author in another paper (i.e., another hyperedge).
  In this work, we introduce a classification of edge-dependent node labels as
a new problem. This problem can be used as a benchmark task for hypergraph
neural networks, which recently have attracted great attention, and also the
usefulness of edge-dependent node labels has been verified in various
applications. To tackle this problem, we propose WHATsNet, a novel hypergraph
neural network that represents the same node differently depending on the
hyperedges it participates in by reflecting its varying importance in the
hyperedges. To this end, WHATsNet models the relations between nodes within
each hyperedge, using their relative centrality as positional encodings. In our
experiments, we demonstrate that WHATsNet significantly and consistently
outperforms ten competitors on six real-world hypergraphs, and we also show
successful applications of WHATsNet to (a) ranking aggregation, (b) node
clustering, and (c) product return prediction.
