Quantum-walk-based search and centrality

We study the discrete-time quantum-walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and the position of the marked vertex, in particular, its centrality. We find that the maximum value of the search probability does not necessarily increase as the marked vertex becomes more central, and we investigate an interesting relationship between the frequency of the successful search probability and the centrality of the marked vertex.