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We introduce and study the spectral evolution model, which characterizes
the growth of large networks in terms of the eigenvalue decomposition of
their adjacency matrices: In large networks, changes over time result in
a change of a graph's spectrum, leaving the eigenvectors unchanged. We
validate this hypothesis for several large social, collaboration,
authorship, rating, citation, communication and tagging networks,
covering unipartite, bipartite, signed and unsigned graphs. Following
these observations, we introduce a link prediction algorithm based on
the extrapolation of a network's spectral evolution. This new link
prediction method generalizes several common graph kernels that can be
expressed as spectral transformations. In contrast to these graph
kernels, the spectral extrapolation algorithm does not make assumptions
about specific growth patterns beyond the spectral evolution model. We
thus show that it performs particularly well for networks with
irregular, but spectral, growth patterns.
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