Privacy Leakage In Graph Signal To Graph Matching Problems

Graph matching over two known graphs is a method for de-anonymizing obscured node labels within an anonymous graph, finding the corresponding nodes in a second graph. In this paper, we consider a new case where a set of graph signals originate from a hidden graph. We want to match their components to a reference graph to reveal labels of asymmetric nodes. We refer to this as the graph-signal-to-graph matching (GS2GM) problem. We introduce a symmetry detection method to pinpoint the asymmetric nodes in the reference graph. Then, we adapt the existing blind graph matching algorithm, originally designed for asymmetric graphs, to align the detected nodes with signals generated from the target hidden graph. Furthermore, we establish sufficient conditions for perfect node de-anonymization through graph signals, showing that graph signals can leak substantial private information on the concealed labels of the underlying graph.