  What are the relations between the edge weights and the topology in
real-world graphs? Given only the topology of a graph, how can we assign
realistic weights to its edges based on the relations? Several trials have been
done for edge-weight prediction where some unknown edge weights are predicted
with most edge weights known. There are also existing works on generating both
topology and edge weights of weighted graphs. Differently, we are interested in
generating edge weights that are realistic in a macroscopic scope, merely from
the topology, which is unexplored and challenging. To this end, we explore and
exploit the patterns involving edge weights and topology in real-world graphs.
Specifically, we divide each graph into layers where each layer consists of the
edges with weights at least a threshold. We observe consistent and surprising
patterns appearing in multiple layers: the similarity between being adjacent
and having high weights, and the nearly-linear growth of the fraction of edges
having high weights with the number of common neighbors. We also observe a
power-law pattern that connects the layers. Based on the observations, we
propose PEAR, an algorithm assigning realistic edge weights to a given
topology. The algorithm relies on only two parameters, preserves all the
observed patterns, and produces more realistic weights than the baseline
methods with more parameters.
