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Statistics of Morphological Finite-State Transition Networks Obey the Power Law

Finite-state devices are widely used in natural language processing, yet little if anything is known about metrics and topology of finite-state transition graphs. Here we study numerically the structure of directed state transition graphs for several types of finite-state devices representing morphology of 16 languages. In all experiments we have found that distribution of incoming and outcoming links is highly skewed and is modeled well by the power law, not by Poisson distribution typical of classical random graphs. The power-law form of degree distribution is regarded as a signature of self-organizing systems, and it has been previously found for numerous real world networks in communication, biology, social sciences and economics.