  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
\cite{barab} are probed. For completeness and comparisons lattice, random,
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 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
whereas the citation networks are tree-like in structure, the metabolic
networks contain many loops.
