  Preferential attachment is one possible way to obtain a scale-free network.
We develop a self-consistent method to determine whether preferential
attachment occurs during the growth of a network, and to extract the
preferential attachment rule using time-dependent data. Model networks are
grown with known preferential attachment rules to test the method, which is
seen to be robust. The method is then applied to a scale-free inherent
structure network, which represents the connections between minima via
transition states on a potential energy landscape. Even though this network is
static, we can examine the growth of the network as a function of a threshold
energy (rather than time), where only those transition states with energies
lower than the threshold energy contribute to the network.For these networks we
are able to detect the presence of preferential attachment, and this helps to
explain the ubiquity of funnels on energy landscapes. However, the scale-free
degree distribution shows some differences from that of a model network grown
using the obtained preferential attachment rules, implying that other factors
are also important in the growth process.
