Impact of structural balance on Self-Avoiding Pruning Walk

Abstract

In a signed network, nodes are connected by two types of logically contradictory links: positive and negative links. These two types of links may play different roles in a dynamic process. In many real-world signed networks, the number of balanced triangles (those that have an odd number of positive links) is higher than that of unbalanced triangles. We refer to the structural balance as the fraction of balanced triangles. In this work, we explore how the structural balance influences a dynamic process. We consider the Self-Avoiding Pruning (SAP) Walk on a signed network which has been recently proposed to model, e.g., a consumer's purchase behavior on a signed product network, where two products can be complementary or competitive with each other (Wang et al., 2017). First, we propose a model to generate signed networks with a given unsigned network topology, a given desired percentage of positive links and structural balance. Second, we design a sign flipping algorithm that could tune the structural balance of a given signed network without changing the percentage of positive links and the underlying topology. Finally, by using both the signed network models and the signed flipped real-world signed networks, we unravel and explain the effect of structural balance on the SAP walk features.