Which Bridges Are Weak Ties? Algebraic Topological Insights on Network Structure and Tie Strength

Abstract

A key question in the analysis of sociological processes on networks is to identify pairs of individuals who have strong or weak social ties. Existing approaches mathematically model the social network as a graph, and tie strength is often inferred by examining the number of shared neighbors between individuals, or equivalently, the number of triangles in the graph which contain a specific pair of individuals. However, this approach misses out on critical information because it does not distinguish the case where interactions occur among groups involving more than two individuals. In this work, we measure tie strength by explicitly accounting for these higher order interactions in the network, through the use of a new measure called Edge PageRank. We show how Edge PageRank can be interpreted as the steady-state outcome of a dynamic, message-passing social process that characterizes the strength of weak ties by appropriately discounting the effect of higher-order interactions involving three individuals. Empirically, we find that Edge PageRank outperforms standard measures in identifying tie strength in several large-scale social networks. These results provide a new perspective on tie strength and demonstrate the importance of incorporating higher-order interactions in social network analysis.

Dynamics on higher-order networks: A review

“…An analytical treatment (Statistically Validated Hypergraphs) is propounded [24] for the problem of finding the most important relationships among the constituents of a higher-order network. Tie strengths are quantified considering higher-order interactions encoded by groups of three or more individuals in social networks by the measure named as 'Edge PageRank' [25]. This measure is proved to be much more efficacious than the traditional approaches for detection of tie strength.…”