Link and triadic closure delay: temporal metrics for social network dynamics

Today, numerous models and metrics are available to capture and characterize static properties of online social networks. When it comes to understanding their dynamics and evolution, however, research offers little in terms of metrics or models. Current metrics are limited to logical time clocks, and unable to capture interactions with external factors that rely on physical time clocks. In this paper, our goal is to take initial steps towards building a set of metrics for characterizing social network dynamics based on physical time. We focus our attention on two metrics that capture the "eagerness" of users in building social structure. More specifically, we propose metrics of link delay and triadic closure delay, two metrics that capture the time delay between when a link or triadic closure is possible, and when they actually instantiate in the trace. Considered over time or across traces, the value of these metrics can provide insight on the speed at which users act in building and extending their social neighborhoods. We apply these metrics to two real traces of social network dynamics from the Renren and Facebook networks. We show that these metrics are generally consistent across networks, but their differences reveal interesting properties of each system. We argue that they can be attributed to factors such as network maturity, environmental and social contexts, and services offered by network provider, all factors independent of the network topology and captured by our proposed metrics. Finally, we find that triadic closure delays capture the ease of neighbor discovery in social networks, and can be strongly influenced by friend recommendation systems.