Title: Randomizing growing networks with a time-respecting null model,
Abstract: Complex networks are often used to represent systems that are not static but
grow with time: people make new friendships, new papers are published and refer
to the existing ones, and so forth. To assess the statistical significance of
measurements made on such networks, we propose a randomization methodology---a
time-respecting null model---that preserves both the network's degree sequence
and the time evolution of individual nodes' degree values. By preserving the
temporal linking patterns of the analyzed system, the proposed model is able to
factor out the effect of the system's temporal patterns on its structure. We
apply the model to the citation network of Physical Review scholarly papers and
the citation network of US movies. The model reveals that the two datasets are
strikingly different with respect to their degree-degree correlations, and we
discuss the important implications of this finding on the information provided
by paradigmatic node centrality metrics such as indegree and Google's PageRank.
The randomization methodology proposed here can be used to assess the
significance of any structural property in growing networks, which could bring
new insights into the problems where null models play a critical role, such as
the detection of communities and network motifs.