Abstract
Topological properties of “scale-free” networks are investigated by determining their spectral dimensions which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model [A.-L. Barabasi and R. Albert, Science 286, 509 (1999)] are probed. For completeness and comparisons lattice, random and small-world models are also investigated. We find that is around for citation and metabolic networks, which is significantly different from the growing network model, for which is approximately This signals a substantial difference in network topology despite the observed similarities in vertex-order distributions. In addition, the diffusion analysis indicates that the citation networks are treelike in structure, whereas the metabolic networks contain many loops.
- Received 19 March 2001
DOI:https://doi.org/10.1103/PhysRevE.64.036106
©2001 American Physical Society