It has been widely recognized since some time already that Nature is full of all kinds of random networks of complex topology, which describe such apparently disparate systems as biological, economical, sociological or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections between the nodes. We shall look at then from the information theory point of view and show that in this way we can easily describe a wide spectrum of possible types of distributions including, in the case of nonextensive version of information theory, the power-like scale-free distributions characterist of complex systems.

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