  We investigate critical behaviors of a social contagion model on weighted
networks. An edge-weight compartmental approach is applied to analyze the
weighted social contagion on strongly heterogenous networks with skewed degree
and weight distributions. We find that degree heterogeneity can not only alter
the nature of contagion transition from discontinuous to continuous but also
can enhance or hamper the size of adoption, depending on the unit transmission
probability. We also show that, the heterogeneity of weight distribution always
hinder social contagions, and does not alter the transition type.
