2009/06/10 by Xin Jiang, Hailong Wang, Lili Ma +5
Mathematics · Physics and Astronomy · #Boson #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Degeneracy (biology) #Excited state #Graph #Ground state #Limit (mathematics) #Mathematical analysis #Mathematics #Node (physics) #Opinion Dynamics and Social Influence #Path (computing) #Physics #Quantum #Quantum mechanics #Random graph #Statistical physics #Theoretical and Computational Physics #Theoretical computer science #Topology (electrical circuits) #physics.soc-ph
paper · pdf · doi:10.1016/j.physa.2010.02.022
4 pages, 3 figures
arxiv created 2009/06/10 · openalex publication_date 2010/02/21 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We introduce a non-interacting boson model to investigate topological structure of complex networks in the present paper. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of real-world networks. We find that the ground state degeneracy of this model is equal to the number of connected components in the network and the square of coefficients in the expansion of ground state gives the averaged time for a random walker spending at each node in the infinite time limit. Furthermore, the first excited state appears always on its largest connected component. To show usefulness of this approach in practice, we carry on also numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods.