  A signed network represents how a set of nodes are connected by two logically
contradictory types of links: positive and negative links. In a signed products
network, two products can be complementary (purchased together) or
substitutable (purchased instead of each other). Such contradictory types of
links may play dramatically different roles in the spreading process of
information, opinion, behavior etc. In this work, we propose a Self-Avoiding
Pruning (SAP) random walk on a signed network to model e.g. a user's purchase
activity on a signed products network. A SAP walk starts at a random node. At
each step, the walker moves to a positive neighbour that is randomly selected
and its previously visited node together with its negative neighbours are
removed. We explored both analytically and numerically how signed network
topological features influence the key performance of a SAP walk: the evolution
of the pruned network resulted from the node removals, the length of a SAP walk
and the visiting probability of each node. These findings in signed network
models are further verified in two real-world signed networks. Our findings may
inspire the design of recommender systems regarding how recommendations and
competitions may influence consumers' purchases and products' popularity.
