  From the spectral plot of the (normalized) graph Laplacian, the essential
qualitative properties of a network can be simultaneously deduced. Given a
class of empirical networks, reconstruction schemes for elucidating the
evolutionary dynamics leading to those particular data can then be developed.
This method is exemplified for protein-protein interaction networks. Traces of
their evolutionary history of duplication and divergence processes are
identified. In particular, we can identify typical specific features that
robustly distinguish protein-protein interaction networks from other classes of
networks, in spite of possible statistical fluctuations of the underlying data.
