Structured thalamocortical connectivity revealed by random walks on   complex networks
  The segregated regions of the mammalian cerebral cortex and thalamus form an extensive and complex network, whose structure and function are still only incompletely understood. The present article describes an application of the concepts of complex networks and random walks that allows the identification of non-random, highly structured features of thalamocortical connections, and their potential effects on dynamic interactions between cortical areas in the cat brain. Utilizing large-scale anatomical data sets of this thalamocortical system, we investigate uniform random walks in such a network by considering the steady state eigenvector of the respective stochastic matrix. It is shown that thalamocortical connections are organized in such a way as to guarantee strong correlation between the outdegree and occupancy rate (a stochastic measure potentially related to activation) of each cortical area. Possible organizational principles underlying this effect are identified and discussed. 
Luciano da Fontoura Costa and Olaf Sporns