  Classical graph matching aims to find a node correspondence between two
unlabeled graphs of known topologies. This problem has a wide range of
applications, from matching identities in social networks to identifying
similar biological network functions across species. However, when the
underlying graphs are unknown, the use of conventional graph matching methods
requires inferring the graph topologies first, a process that is highly
sensitive to observation errors. In this paper, we tackle the blind graph
matching problem with unknown underlying graphs directly using observations of
graph signals, which are generated from graph filters applied to graph signal
excitations. We propose to construct sample covariance matrices from the
observed signals and match the nodes based on the selected sample eigenvectors.
Our analysis shows that the blind matching outcome converges to the result
obtained with known graph topologies when the signal sampling size is large and
the signal noise is small. Numerical results showcase the performance
improvement of the proposed algorithm compared to matching two estimated
underlying graphs learned from the graph signals.
