Hubiness, length, crossings and their relationships in dependency trees
This work provides theoretical insights into linguistic structures, potentially impacting natural language processing by linking tree properties to cognitive costs, though it is incremental in nature.
The study analyzed dependency trees through hubiness, mean dependency length, and dependency crossings, deriving bounds that show pairwise dependencies among these metrics. It found that hubiness bounds mean dependency length from below and crossings from above, suggesting that sentence memory cost may depend on hubiness as well as word ordering.
Here tree dependency structures are studied from three different perspectives: their degree variance (hubiness), the mean dependency length and the number of dependency crossings. Bounds that reveal pairwise dependencies among these three metrics are derived. Hubiness (the variance of degrees) plays a central role: the mean dependency length is bounded below by hubiness while the number of crossings is bounded above by hubiness. Our findings suggest that the online memory cost of a sentence might be determined not just by the ordering of words but also by the hubiness of the underlying structure. The 2nd moment of degree plays a crucial role that is reminiscent of its role in large complex networks.