  In this paper we propose some new measures of language development using
network analyses, which is inspired by the recent surge of interests in network
studies of many real-world systems. Children's and care-takers' speech data
from a longitudinal study are represented as a series of networks, word forms
being taken as nodes and collocation of words as links. Measures on the
properties of the networks, such as size, connectivity, hub and authority
analyses, etc., allow us to make quantitative comparison so as to reveal
different paths of development. For example, the asynchrony of development in
network size and average degree suggests that children cannot be simply
classified as early talkers or late talkers by one or two measures. Children
follow different paths in a multi-dimensional space. They may develop faster in
one dimension but slower in another dimension. The network approach requires
little preprocessing of words and analyses on sentence structures, and the
characteristics of words and their usage emerge from the network and are
independent of any grammatical presumptions. We show that the change of the two
articles "the" and "a" in their roles as important nodes in the network
reflects the progress of children's syntactic development: the two articles
often start in children's networks as hubs and later shift to authorities,
while they are authorities constantly in the adult's networks. The network
analyses provide a new approach to study language development, and at the same
time language development also presents a rich area for network theories to
explore.
