  Real-world networks process structured connections since they have
non-trivial vertex degree correlation and clustering. Here we propose a toy
model of structure formation in real-world weighted network. In our model, a
network evolves by topological growth as well as by weight change. In addition,
we introduce the weighted assortativity coefficient, which generalizes the
assortativity coefficient of a topological network, to measure the tendency of
having a high-weighted link between two vertices of similar degrees. Network
generated by our model exhibits scale-free behavior with a tunable exponent.
Besides, a few non-trivial features found in real-world networks are reproduced
by varying the parameter ruling the speed of weight evolution. Most
importantly, by studying the weighted assortativity coefficient, we found that
both topologically assortative and disassortative networks generated by our
model are in fact weighted assortative.
