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Markov Processes and Brain Network Hubs.

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Bibliographic Details
Title:	Markov Processes and Brain Network Hubs.
Authors:	Murty, M. Ram¹ (AUTHOR) murty@queensu.ca, Prasad, Asuri Narayan² (AUTHOR) narayan.prasad@lhsc.on.ca
Source:	Resonance: Journal of Science Education. Jun2026, Vol. 31 Issue 6, p859-884. 26p.
Subject Terms:	Markov processes, Graph theory, Large-scale brain networks, Eigenvalues, Ergodic theory, Brain mapping, Brain imaging
Abstract:	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, neural network models involve distributed neural circuits of nodes, hubs, and connections that are dynamic across 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 have limitations and inconsistencies in the results they achieve. 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 discrete 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. [ABSTRACT FROM AUTHOR]
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Database:	Education Research Complete

Description
Abstract:	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, neural network models involve distributed neural circuits of nodes, hubs, and connections that are dynamic across 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 have limitations and inconsistencies in the results they achieve. 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 discrete 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. [ABSTRACT FROM AUTHOR]
ISSN:	09718044
DOI:	10.1007/s12045-026-2012-5