  In this chapter we give an overview of the application of complex network
theory to quantify some properties of language. Our study is based on two
fables in Ukrainian, Mykyta the Fox and Abu-Kasym's slippers. It consists of
two parts: the analysis of frequency-rank distributions of words and the
application of complex-network theory. The first part shows that the text sizes
are sufficiently large to observe statistical properties. This supports their
selection for the analysis of typical properties of the language networks in
the second part of the chapter. In describing language as a complex network,
while words are usually associated with nodes, there is more variability in the
choice of links and different representations result in different networks.
Here, we examine a number of such representations of the language network and
perform a comparative analysis of their characteristics. Our results suggest
that, irrespective of link representation, the Ukrainian language network used
in the selected fables is a strongly correlated, scale-free, small world. We
discuss how such empirical approaches may help form a useful basis for a
theoretical description of language evolution and how they may be used in
analyses of other textual narratives.
