Roles of Ties in Spreading

Background : Controlling global epidemics in the real world and accelerating information propagation in the artificial world are of great significance, which have activated an upsurge in the studies on networked spreading dynamics. Lots of efforts have been made to understand the impacts of macroscopic statistics (e.g., degree distribution and average distance) and mesoscopic structures (e.g., communities and rich clubs) on spreading processes while the microscopic elements are less concerned. In particular, roles of ties are not yet clear to the academic community. Methodology/Principle Findings : Every edges is stamped by its strength that is defined solely based on the local topology. According to a weighted susceptible-infected-susceptible model, the steady-state infected density and spreading speed are respectively optimized by adjusting the relationship between edge’s strength and spreading ability. Experiments on six real networks show that the infected density is increased when strong ties are favored in the spreading, while the speed is enhanced when weak ties are favored. Significance of these findings is further demonstrated by comparing with a null model. Conclusions/Significance: Experimental results indicate that strong and weak ties play distinguishable roles in spreading dynamics: the former enlarge the infected density while the latter fasten the process. The proposed method provides a quantitative way to reveal the qualitatively different roles of ties, which could find applications in analyzing many networked dynamical processes with multiple performance indices, such as synchronizability and converging time in synchronization and throughput and delivering time in transportation. Introduction Early before the classification of social ties proposed, in 1954, the Russian mathematical psychologist Anatol Rapoport [1] has been aware of “well-known fact that the likely contacts of two individuals who are closely acquainted tend to be more overlapping than those of two arbitrarily selected individuals.” This argument became one of the cornerstones of social network theory. In 1973, ties in social networks, generally, come in two varieties: strong and weak, which has been first proposed by the American sociologist Mark Granovetter in Ref. [2], one of the most influential sociology papers ever published. Different relationships can be measured in the currency of tie strength. According to the closeness, connections to close friends have been said to be “strong” ties, while those to acquaintances have been called “weak” ties [2–6]. Tie strength usually plays an vital role in many real networks and is crucial to understand dynamical processes on the networks [6–8]. Strong ties are the people you really trust, people whose social circles tightly overlap with your own. Often, they are also the people most like you. Weak ties, conversely, are merely acquaintances and often provide access to novel information [6]. Weak ties display an important bridging function [7], while strong ties are more likely to activated for the flow of referral information and more influential than weak ties [8]. In addition, weak ties could play a more significant role than strong ties to keep the stability [9], maintain the connectivity [10] and uncover the missing information [11]. In despite of the qualitative distinction between strong and weak ties, the tie strength could be quantitatively described by edge weight—the edges with high weights are considered to be strong. In a number of social networks, edges are often associated with weights that differentiate them in terms of their