  Nowadays, the emergence of online services provides various multi-relation
information to support the comprehensive understanding of the epidemic
spreading process. In this Letter, we consider the edge weights to represent
such multi-role relations. In addition, we perform detailed analysis of two
representative metrics, outbreak threshold and epidemic prevalence, on SIS and
SIR models. Both theoretical and simulation results find good agreements with
each other. Furthermore, experiments show that, on fully mixed networks, the
weight distribution on edges would not affect the epidemic results once the
average weight of whole network is fixed. This work may shed some light on the
in-depth understanding of epidemic spreading on multi-relation and weighted
networks.
