  Identifying power-law scaling in real networks - indicative of preferential
attachment - has proved controversial. Critics argue that measuring the
temporal evolution of a network directly is better than measuring the degree
distribution when looking for preferential attachment. However, many of the
established methods do not account for any potential time-dependence in the
attachment kernels of growing networks, or methods assume that node degree is
the key observable determining network evolution. In this paper, we argue that
these assumptions may lead to misleading conclusions about the evolution of
growing networks. We illustrate this by introducing a simple adaptation of the
Barab{\'a}si-Albert model, the "k2 model", where new nodes attach to nodes in
the existing network in proportion to the number of nodes one or two steps from
the target node. The k2 model results in time dependent degree distributions
and attachment kernels, despite initially appearing to grow as linear
preferential attachment, and without the need to include explicit time
dependence in key network parameters (such as the average out-degree). We show
that similar effects are seen in several real world networks where constant
network growth rules do not describe their evolution. This implies that
measurements of specific degree distributions in real networks are also likely
to change over time.

Physics and Society