  Current concepts of neural networks have emerged over two centuries of
progress beginning with the neural doctrine to the idea of neural cell
assemblies. Presently the model of neural networks involves distributed neural
circuits of nodes, hubs, and connections that are dynamic in different states
of brain function. Advances in neurophysiology, neuroimaging and the field of
connectomics have given impetus to the application of mathematical concepts of
graph theory. Current approaches do carry limitations and inconsistency in
results achieved. We model the neural network of the brain as a directed graph
and attach a matrix (called the Markov matrix) of transition probabilities
(determined by the synaptic strengths) to every pair of distinct nodes giving
rise to a (continuous) Markov process. We postulate that the network hubs are
the nodes with the highest probabilities given by the stationary distribution
of Markov theory. We also derive a new upper bound for the diameter of a graph
in terms of the eigenvalues of the Markov matrix.
