Hubiness, length, crossings and their relationships in dependency trees

TL;DR

This paper investigates the relationships among hubiness, dependency length, and crossings in dependency trees, revealing bounds and the influential role of degree variance in linguistic and network structures.

Contribution

It introduces bounds linking hubiness, dependency length, and crossings, highlighting the importance of degree variance in dependency structures and language processing.

Findings

Mean dependency length is bounded below by hubiness.

Number of crossings is bounded above by hubiness.

Degree variance influences structural complexity in dependency trees.

Abstract

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.