  In this paper, we measure the privacy leakage via studying whether graph
representations can be inverted to recover the graph used to generate them via
graph reconstruction attack (GRA). We propose a GRA that recovers a graph's
adjacency matrix from the representations via a graph decoder that minimizes
the reconstruction loss between the partial graph and the reconstructed graph.
We study three types of representations that are trained on the graph, i.e.,
representations output from graph convolutional network (GCN), graph attention
network (GAT), and our proposed simplicial neural network (SNN) via a
higher-order combinatorial Laplacian. Unlike the first two types of
representations that only encode pairwise relationships, the third type of
representation, i.e., SNN outputs, encodes higher-order interactions (e.g.,
homological features) between nodes. We find that the SNN outputs reveal the
lowest privacy-preserving ability to defend the GRA, followed by those of GATs
and GCNs, which indicates the importance of building more private
representations with higher-order node information that could defend the
potential threats, such as GRAs.
