Determining Influential Edges with Higher Order Information

Social capital, which refers to the resources an individual has due to their position in a social structure, is critical for individual and organizational success in many settings.  In this work, we focus on the task of identifying important edges in a social network, in order to determine how one can optimally utilize their social capital. Previous work has taken two similar but distinct approaches to this task, both of which model the social network as a graph. The first approach highlights the “strength of weak ties,” and states that the most useful information in one’s social network comes from acquaintances (weak ties) who may have access to more novel sources of information, as opposed to close friends (strong ties) who may carry redundant information. The second approach suggests that important connections are those which act as bridges in a network and that individuals with the most social capital are those whose contacts span “structural holes” in the social network. 
 
Here, we propose the use of the Edge PageRank measure (Schaub et al. 2019) to identify important edges in a social network and find that it unifies and extends the two aforementioned approaches in the literature. Rather than model the social network as a graph, we model the network as a simplicial complex that has the capacity to incorporate higher-order interactions between groups of 3 or more individuals. We then use a stochastic process analogous to PageRank to determine a centrality score for edges. From a theoretical perspective, we find that Edge PageRank formalizes the notion of structural holes using tools from algebraic topology, and from an empirical standpoint, we find that Edge PageRank outperforms graph-based measures in identifying tie strength across several large scale social networks.
 
This is joint work with Jean-Baptiste Seby, Austin Benson, and Ali Jadbabaie. The relevant pre-print can be found here.