Detecting the structure of complex networks by quantum bosonic dynamics

In this paper, we introduce a non-interacting boson model to investigate the topological structure of complex networks. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of realistic networks. We find that the ground-state degeneracy of this model is equal to the number of connected components in a network and the square of each coefficient in the expansion of the ground state gives the average time that a random walker spends at each node in the infinite time limit. To show the usefulness of this approach in practice, we also carry out numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods. Furthermore, we show that the first excited state appears always on the largest connected component of the network. The relationship between the first excited energy and the average shortest path length in networks is also discussed.