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 users 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.
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