We are analyzing https://link.springer.com/article/10.1186/1753-4631-1-3.

Title:
Graph theoretical analysis of complex networks in the brain | Nonlinear Biomedical Physics
Description:
Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the
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Keywords {🔍}

networks, network, google, scholar, article, smallworld, random, graph, brain, functional, connectivity, analysis, degree, ads, complex, graphs, path, scalefree, study, authors, synchronization, clustering, length, edges, showed, dynamics, structure, studied, studies, synchronizability, coefficient, vertices, phys, neurons, properties, model, measures, rev, weighted, theory, vertex, optimal, time, activity, number, neural, eeg, function, small, architecture,

Topics {✒️}

clear-cut small-world pattern cond-mat/0001118j v2 article google scholar excitable fitzhugh-nagumo neurons article download pdf van den berg eeg slow-wave activity explicit time-frequency priors small-world parameter σ economic small-world behavior multi-channel eeg recordings 1000 coupled fitzhugh-nagumo normal small-world configuration frequency-dependent functional connectivity optimal small-world configuration small-world metric defined auto-associative retrieval diversity-induced synchronized oscillations optimal small-world pattern scale-free network regime small-world brain networks scale-free degree distribution privacy choices/manage cookies medial temporal lobe called 'small-world' networks healthy small-world network weighted small-world network long-range temporal correlations small-world anatomical networks display rapid task-related showed small-world characteristics small-world network organization scale-free degree distributions small-world model synchronized strogatz small-world model small-world networks showed eyes-open state 12 hindmarsh-rose neurons temporal lobe architecture multi channel recordings temporal coherent oscillations full size image 𝑖 𝑘 𝑖 extract nonlinear properties van dijk bw els van deventer small-world features eigenvalue ratio λn/λ2 𝑚 𝑎 𝑖 strychnine-induced dysinhibition

Questions {❓}

(iii) which network factors provide the best explanation for cognitive functioning?
(vi) is there a relationship between the 'giant cluster' which emerges at the onset of synchronization and consciousness?
Brenner RP: Is it Status?
Nishikawa T, Motter AE, Lai Y-Ch, Hoppensteadt FC: Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?
Some of the questions that have to be addressed by new studies are the following: (i) how does network structure change during growth and development?
Stam CJ: Functional connectivity patterns of human magnetoencephalographic recordings: a "small-world" network?

Schema {🗺️}

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      headline:Graph theoretical analysis of complex networks in the brain
      description:Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.
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         Gamma Band
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