## Hersenweb

The application of modern network theory to the brain is a relatively new development. The number of papers on this topic is increasing rapidly, and it is not easy even for experts to keep an overview of ongoing developments. Because brain network science is new and evolving rapidly, little is known about it by the general audience. To inform a general non specialist but interested public about the exciting field of brain network science we (Kees Stam, Linda Douw and Willem de Haan) have written a book “Hersenweb”, published by Bert Bakker / Prometheus. In ten chapters the book gives an overview of the development and history of brain network science, explains the basics of graph theory and brain connectivity and sketches applications to healthy subjects and a variety of brain disorders, including Alzheimer’s disease, brain tumours, schizophrenia and epilepsy. If you have read the book and want to comment on it please let us know.

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## Books on graph theory and modern network theory

The modern theory of networks is a branch of mathematical graph theory that has a long history going all the way back to Leonhard Euler (1707-1783) who solved the problem of the seven bridges of Konigsberg in 1736. Graph theory only became relevant for the study of large complex networks with the discovery of “small-world” networks by Duncan J. Watts and Steven Strogatz in 1998, and the discovery of “scale-free” networks by Barabasi and Albert in 1999. In his popular book “Sync” Strogatz gives a description of the discovery of “small-world” networks and their relation to the more general problem of synchronization in large systems of oscillators. Duncan Watts has also written a popular book about network analysis: “Six degrees”. The discovery of “scale-free” networks and their significance is described by Barabasi in his book “Linked”. The merit of these three books is that they are written by the scientists who created modern network theory and give a first hand account of an exciting series of discoveries. There are also very good popular science book on networks by science journalists. For instance, the book “Small world” by Mark Buchan can be highly recommended. Another “must read” is the book “Complexity” by complexity scientist Melanie Mitchell, who places network theory in the wider context of complexity science. A brilliant book about the application of game theory to evolutionary dynamics is "Supercooperators" by Martin Nowak and Roger Highfield. Although it is not really about the brain, the highly original discussion of how large "communities" of "agents" can and will cooperate may be more relevant for brain network science than is currently appreciated. Will games on brain networks be the new way to go?

Several excellent textbooks on modern network theory have been published recently. Maarten van Steen from the VU in Amsterdam has written “Graph theory and complex networks: an introduction”. This is a very good introductory text. It can be bought as a conventional book, or downloaded for free from the website of the author. A more extensive overview of modern network theory can be found in the book “Networks: an introduction” by Mark Newman, who is currently one of the most active scientists in the field. Other books deal with more specific aspects of network theory. The book “Dynamical processes on complex networks” by Barrat, Barthelemy and Vespignani focuses on the interaction between network topology and dynamical processes taking place on these networks. This book contains a chapter on “Networks in biology: from cells to ecosystems”. A text that emphasizes the evolution of complex networks is the book“Evolution of networks. From biological nets to the Internet and WWW” by S.N. Dorogovtsev and J.F.F. Mendes. The application of graph spectral analysis to the study of complex networks is described by Piet Van Mieghem from the Technical University of Delft in his recent book “Graph spectra for complex networks”. A comprehensive overview of modern network analysis and its applications can be found in the book by Ernesto Estrada "The structure of complex networks"

## Books on structural and functional connectivity and networks in the brain

A central problem in neuroscience is the question how different parts of the brain communicate. This problem, often referred to as functional connectivity, is older than the application of graph theory to the brain. Several books give a nice overview of this field. The “Handbook of brain connectivity” contains many useful discussions of brain connectivity from different points of view, ranging from mathematical modeling to clinical applications. It is an important book, but it is quite technical, and lacks a single overall vision of communication in the brain. A comparable book is “Coordinated activity in the brain” edited by Jose Luis Perez Velazquez and Richard Wennberg. This book contains two chapters on the application of network theory to the brain. Currently, the most important book about network theory and the brain is “Networks of the brain” by Olaf Sporns. Sporns is a pioneer in this field, and his book gives a very readable an appealing overview of graph theory and its many applications to neuroscience. This book is especially useful for neuroscientists who want to learn about network theory, and is very suited for introductory courses in this field.

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