UC Davis

Graph matching over two given graphs is a well-established method for re-identifying obscured node labels within an anonymous graph by matching the corresponding nodes in a reference graph. This paper studies a new application, termed the graph-signal-to-graph matching (GS2GM) problem, where the attacker observes a set of filtered graph signals originating from a hidden graph. These signals are generated through an unknown graph filter activated by certain input excitation signals. Our goal is to match their components to a labeled reference graph to reveal the labels of asymmetric nodes in this unknown graph, where the excitations can be either known or unknown to the attacker. To this end, we integrate the existing blind graph matching algorithm with techniques of graph filter inference and covariance-based eigenvector estimation. 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. Experimental results validate our theoretical insights and demonstrate that the proposed attack effectively reveals many of the hidden labels, particularly when the graph signals are adequately uncorrelated and sampled.