  Relationships between individuals in a social network, genes in biological
systems, and spins in magnetic systems often reflect a mixture of positive
(friendly) and negative (antagonistic) interactions. However, most studies of
complex networks have focused on networks consisting of solely positive
interactions. Here, we study threshold cascades on signed networks composed of
both positive and negative connections, focusing on when a pair of nodes
connected by a negative link can only be activated exclusively to each other.
We found that the negative interactions not only suppress global cascades, but
also induce the heterogeneity in activation patterns manifesting from
single-node to network levels. Our results suggest that negative interactions
may be an important source of the variability in cascading dynamics.
