  The geometric renormalization technique for complex networks has successfully
revealed the multiscale self-similarity of real network topologies and can be
applied to generate replicas at different length scales. In this letter, we
extend the geometric renormalization framework to weighted networks, where the
intensities of the interactions play a crucial role in their structural
organization and function. Our findings demonstrate that weights in real
networks exhibit multiscale self-similarity under a renormalization protocol
that selects the connections with the maximum weight across increasingly longer
length scales. We present a theory that elucidates this symmetry, and that
sustains the selection of the maximum weight as a meaningful procedure. Based
on our results, scaled-down replicas of weighted networks can be
straightforwardly derived, facilitating the investigation of various
size-dependent phenomena in downstream applications.
