  Network centrality has important implications well beyond its role in
physical and information transport analysis; as such, various quantum
walk-based algorithms have been proposed for measuring network vertex
centrality. In this work, we propose a continuous-time quantum walk algorithm
for determining vertex centrality, and show that it generalizes to arbitrary
graphs via a statistical analysis of randomly generated scale-free and
Erd\H{o}s-R\'enyi networks. As a proof of concept, the algorithm is detailed on
a 4-vertex star graph and physically implemented via linear optics, using
spatial and polarization degrees of freedoms of single photons. This paper
reports the first successful physical demonstration of a quantum centrality
algorithm.
