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.

Many systems are dynamic and time-varying in the real world. Discovering the vital nodes in temporal networks is more challenging than that in static networks. In this study, we proposed a temporal information gathering (TIG) process for temporal networks. The TIG-process, as a node's importance metric, can be used to do the node ranking. As a framework, the TIG-process can be applied to explore the impact of temporal information on the significance of the nodes. The key point of the TIG-process is that nodes' importance relies on the importance of its neighborhood. There are four variables: temporal information gathering depth n, temporal distance matrix D, initial information c, and weighting function f. We observed that the TIG-process can degenerate to classic metrics by a proper combination of these four variables. Furthermore, the fastest arrival distance based TIG-process (fad-tig) is performed optimally in quantifying nodes' efficiency and nodes' spreading influence. Moreover, for the fad-tig process, we can find an optimal gathering depth n that makes the TIG-process perform optimally when n is small.