Central Nodes Detection from Partially Observed Graph Signals

This paper focuses on detecting the central nodes in a graph from partially observed graph signals with unknown graph topology. We follow a general model which considers observed data as filtered graph signals with excitation driven from some external sources shaped by a possibly low-rank influence matrix. To identify the full centrality vector, we rely on the key observation that the vector is embedded in a linear system with the influence matrix. We provide the necessary and sufficient conditions for the centrality vector to be uniquely recovered. Notably, among other requirements, our conditions show that the number of external sources needs to be larger than the number of hidden nodes. Finally, we design an alternating minimization algorithm to estimate centrality vectors from the partially observed signals. Numerical results support our findings.