Algebraic topological characterizations of tie strength in higher-order social networks

The association between tie strength and network structure is a fundamental topic in the analysis of complex social systems. We study this association by analyzing tie strength using higher-order networks, an increasingly relevant model which can encode group interactions between three or more individuals. First, we introduce three measures based on algebraic topology which characterize the network context and influence of an edge. Our experimental results across 15 datasets indicate that these measures outperform standard network proxies in estimating tie strength as a function of the unweighted network topology. These measures can further replicate and explain a puzzle wherein certain bridging ties are surprisingly strong. We then consider a single centrality measure which combines the three initial measures, is highly inversely correlated with tie strength, and can be interpreted through an information exchange process that highlights ties that have access to useful information. In this sense, we are able to illuminate the information advantages of weak ties due to their network position.