I am interested in studying the anatomical and functional connectivity of human brain using graphs, and their evolution in time. This can be used to distinguish different states in which the brain exists at different times - say, executive tasks, meditation, focused attention such as in video games, etc. I am looking for a good reference book (well-written and with practical examples of the concepts) on how the matrices describing the different types of connectivity can be analyzed and manipulated to extract different kinds of information.
These are some of the 'standard' books in algebraic graph theory:
- https://www.springer.com/gp/book/9781447165682
- (see Chapter 6) https://www.routledge.com/Handbook-of-Graph-Theory/Gross-Yellen-Zhang/p/book/9781439880180
You can look into my book : " A tryst with Matrices : The Matrix Shell Model formalism ", published by 24by7 Publishing, India. Although it does not deal with application of matrices to graph connectivity, it deals with a certain way of visualization of matrix itself as a unit of composite structure built of repeating abstract substructures (Matrix Shells), where manipulation of the matrix elements can bring about changes in properties and parameters associated with these abstract substructures (associated State -Interaction matrix descriptions and their corresponding eigenvalues), this framework may be of some relevance and use to the research problem you mention in the post.
Have a look at https://www.fishpond.com.au/Books/Topics-Algebraic-Graph-Theory-Lowell-W-Beineke-Edited-by-Robin-J-Wilson-Edited-by/9780521801973?utm_source=googleps&utm_medium=ps&utm_campaign=AU&gclid=Cj0KCQjwnv71BRCOARIsAIkxW9EiFVasDABpNaqlsoLWwX9tOQGc9fJG1cwcdphMwuIAzYCW9Lj4D9UaAlw4EALw_wcB
https://www.thenile.com.au/books/narsingh-deo/graph-theory-with-applications-to-engineering-and-computer-s/9780486807935?gclid=Cj0KCQjwnv71BRCOARIsAIkxW9F5XM4lvg16ZUe7fGutpnbS-AOFJ5E5BPaAB1U_NgMhCphSYY78r0QaAi5lEALw_wcB and Book is attached.
Thanks a lot Nicholas, Debopam, and Muhammad ! I really appreciate your taking the time and interest to give me these suggestions.
Regards
Ramakrishnan
Dear colleague, some hints:
- Graph Classification And Clustering Based On Vector Space Embedding
By Kaspar Riesen, Horst Bunke
https://www.worldscientific.com/worldscibooks/10.1142/7731#t=toc
- https://sites.google.com/site/bctnet/
- https://www.hindawi.com/journals/cin/2012/412512/
- In our own dept. dr Marieke van Vugt is doing brain-activity analysis in meditation and in Tibetan monk argumentation.
Article Inter-brain Synchronization in the Practice of Tibetan Monastic Debate
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