Topological properties of citation and metabolic networks

Topological properties of “scale-free” networks are investigated by determining their spectral dimensions $d_S,$ 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 $d_S$ is around $3$ for citation and metabolic networks, which is significantly different from the growing network model, for which $d_S$ is approximately $\mathrm{7.5.}$ 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.