This short survey the reviews recent literature on brain connectivity studies. It encompasses all forms of static and dynamic connectivity whether anatomical, functional, or effective. The last decade has seen an ever increasing number of studies devoted to deduce functional or effective connectivity, mostly from functional neuroimaging experiments. Resting state conditions have become a dominant experimental paradigm, and a number of resting state networks, among them the prominent default mode network, have been identified. Graphical models represent a convenient vehicle to formalize experimental findings and to closely and quantitatively characterize the various networks identified. Underlying these abstract concepts are anatomical networks, the so-called connectome, which can be investigated by functional imaging techniques as well. Future studies have to bridge the gap between anatomical neuronal connections and related functional or effective connectivities. 1. Brain Connectivity—What It Is All About The functional organization of the brain is characterized by segregation and integration of information being processed. A central paradigm in modern neuroscience is that anatomical and functional connections between brain regions are organized in a way such that information processing is near optimal. Functional interactions seem to be provided by synchronized activity, both locally and between distant brain regions. Brain networks thus consist of spatially distributed but functionally connected regions that process information. Brain connectivity analysis rests upon three different but related forms of connectivity .(i)Anatomical connectivity (AC), also called structural connectivity, which forms the connectome  through synaptic contacts between neighboring neurons or fiber tracks connecting neuron pools in spatially distant brain regions. The whole set of such fiber tracks in the brain is called white matter. On short time scales (sec, min), anatomical connections are quite persistent and stable, while for longer time spans substantial plasticity may be observed. (ii)Functional connectivity (FC) which is defined as the temporal dependency of neuronal activation patterns of anatomically separated brain regions. It reflects statistical dependencies between distinct and distant regions of information processing neuronal populations. Hence, it is basically a statistical concept which relies on such statistical measures as correlation, covariance, spectral coherence, or phase locking. Statistical dependencies are highly time dependent and
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