Truncation of power law behavior in "scale-free" network models due to   information filtering
  We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the distribution of the number of incoming links to a node follows a universal scaling form, i.e., that it decays as a power law with an exponential truncation controlled not only by the system size but also by a feature not previously considered, the subset of the network ``accessible'' to the node. We test our model with empirical data for the World Wide Web and find agreement. 
Stefano Mossa, Marc Barthelemy, H. Eugene Stanley, and Luis A. Nunes   Amaral