Self-organization of the Sound Inventories: Analysis and Synthesis of the Occurrence and Co-occurrence Networks of Consonants∗

Abstract

The sound inventories of the world's languages self-organize themselves, giving rise to similar cross-linguistic patterns. In this work, we attempt to capture this phenomenon of self-organization, which shapes the structure of the consonant inventories, through a complex network approach. For this purpose we define the occurrence and co-occurrence networks of consonants and systematically study some of their important topological properties. A crucial observation is that the occurrence as well as the co-occurrence of consonants across languages follows a power law distribution. This property is arguably a consequence of the principle of preferential attachment. In order to support this argument we propose a synthesis model, which reproduces the degree distribution for the networks to a close approximation. We further observe that the co-occurrence network of consonants shows a high degree of clustering and subsequently refine our synthesis model in order to explain this property. Finally, we discuss how preferential attachment manifests itself through the evolutionary nature of language.

Acknowledgements

AM would like to thank Microsoft Research India for financial assistance. All the authors would like to extend their gratitude to Reinhard Köhler for his valuable comments and suggestions.

Notes

¹From a bipartite network, one can construct its unipartite counterpart, the so-called one-mode projection onto actors, as a network consisting solely of the social actors as nodes, two of which are connected by an edge for each social tie they both participate in. For example, two consonant nodes in the one-mode projection are connected as many times as they have co-occurred across the language inventories.

²A random variable is said to have a β-distribution with parameters α > 0 and β > 0 if and only if its probability mass function is given by,

for 0 < x < 1 and f(x) = 0 otherwise. Γ(·) is the Euler's gamma function.

³Mean error is defined as the average difference between the ordinate pairs (say y and y′), where the abscissas are equal. In other words, if there are N such ordinate pairs then the mean error can be expressed as

⁴The error in the average clustering coefficient is expressed as

where c_av and c′_av are the average clustering coefficients of PhoNet and PhoNet _syn respectively.

⁵There is a very little chance of reformation of the bond, only if by coincidence the speakers learn a foreign language which has in its inventory one of the consonants lost (from the inventory of the native language of the speaker) in the process of language change.