Brain anatomical networks are sparse, complex, and have economical small-world properties. We investigated the efficiency and cost of human brain functional networks measured using functional magnetic resonance imaging (fMRI) in a factorial design: two groups of healthy old (N = 11; mean age = 66.5 years) and healthy young (N = 15; mean age = 24.7 years) volunteers were each scanned twice in a no-task or “resting” state following placebo or a single dose of a dopamine receptor antagonist (sulpiride 400 mg). Functional connectivity between 90 cortical and subcortical regions was estimated by wavelet correlation analysis, in the frequency interval 0.06–0.11 Hz, and thresholded to construct undirected graphs. These brain functional networks were small-world and economical in the sense of providing high global and local efficiency of parallel information processing for low connection cost. Efficiency was reduced disproportionately to cost in older people, and the detrimental effects of age on efficiency were localised to frontal and temporal cortical and subcortical regions. Dopamine antagonism also impaired global and local efficiency of the network, but this effect was differentially localised and did not interact with the effect of age. Brain functional networks have economical small-world properties—supporting efficient parallel information transfer at relatively low cost—which are differently impaired by normal aging and pharmacological blockade of dopamine transmission.

Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequencydependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03-0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.

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Brain function depends on adaptive self-organization of largescale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequencyspecific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a fingertapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by smallworld properties at all six wavelet scales considered, corresponding approximately to classical ␦ (low and high), , ␣, ␤, and ␥ frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2-37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency ␥ network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both ␤ and ␥ networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters. magnetoencephalography ͉ wavelet ͉ graph theory ͉ connectivity ͉ binding C oherent or correlated oscillation of large-scale, distributed neural networks is widely regarded as an important physiological substrate for motor, perceptual and cognitive representations in the brain (1, 2). The topological description of brain networks promises quantitative insight into functionally relevant parameters because their topology strongly influences their dynamic properties such as speed and specialization of information processing, learning, and robustness against pathological attack by disease (3).The topology of networks can range from entirely random to fully ordered (a lattice). In this spectrum, small-world topology is characteristic of complex networks that demonstrate both clustered or cliquish interconnectivity within groups of nodes sharing many nearest neighbors in common (like regular lattices), and a short path length between any two nodes in the network (like random graphs) (3). This is an attractive configuration, in principle, for the anatomical and functional architecture of the brain, because small-world networks are known to optimize information transfer, increase the rate of learning, and support both segregated and...

Human brain networks have topological properties in common with many other complex systems, prompting the following question: what aspects of brain network organization are critical for distinctive functional properties of the brain, such as consciousness? To address this question, we used graph theoretical methods to explore brain network topology in resting state functional MRI data acquired from 17 patients with severely impaired consciousness and 20 healthy volunteers. We found that many global network properties were conserved in comatose patients. Specifically, there was no significant abnormality of global efficiency, clustering, small-worldness, modularity, or degree distribution in the patient group. However, in every patient, we found evidence for a radical reorganization of high degree or highly efficient "hub" nodes. Cortical regions that were hubs of healthy brain networks had typically become nonhubs of comatose brain networks and vice versa. These results indicate that global topological properties of complex brain networks may be homeostatically conserved under extremely different clinical conditions and that consciousness likely depends on the anatomical location of hub nodes in human brain networks.connectome | consciousness disorders | neuroimaging | wavelet | brain injury

Endophenotypes (intermediate phenotypes) are objective, heritable, quantitative traits hypothesized to represent genetic risk for polygenic disorders at more biologically tractable levels than distal behavioural and clinical phenotypes. It is theorized that endophenotype models of disease will help to clarify both diagnostic classification and aetiological understanding of complex brain disorders such as obsessive-compulsive disorder (OCD). To investigate endophenotypes in OCD, we measured brain structure using magnetic resonance imaging (MRI), and behavioural performance on a response inhibition task (Stop-Signal) in 31 OCD patients, 31 of their unaffected first-degree relatives, and 31 unrelated matched controls. Both patients and relatives had delayed response inhibition on the Stop-Signal task compared with healthy controls. We used a multivoxel analysis method (partial least squares) to identify large-scale brain systems in which anatomical variation was associated with variation in performance on the response inhibition task. Behavioural impairment on the Stop-Signal task, occurring predominantly in patients and relatives, was significantly associated with reduced grey matter in orbitofrontal and right inferior frontal regions and increased grey matter in cingulate, parietal and striatal regions. A novel permutation test indicated significant familial effects on variation of the MRI markers of inhibitory processing, supporting the candidacy of these brain structural systems as endophenotypes of OCD. In summary, structural variation in large-scale brain systems related to motor inhibitory control may mediate genetic risk for OCD, representing the first evidence for a neurocognitive endophenotype of OCD.

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunc- tions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network prop- erties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

The exploration of brain networks with resting-state fMRI (rs-fMRI) combined with graph theoretical approaches has become popular, with the perspective of finding network graph metrics as biomarkers in the context of clinical studies. A preliminary requirement for such findings is to assess the reliability of the graph based connectivity metrics. In previous test-retest (TRT) studies, this reliability has been explored using intraclass correlation coefficient (ICC) with heterogeneous results. But the issue of sample size has not been addressed. Using the large TRT rs-fMRI dataset from the Human Connectome Project (HCP), we computed ICCs and their corresponding p-values (applying permutation and bootstrap techniques) and varied the number of subjects (from 20 to 100), the scan duration (from 400 to 1200 time points), the cost and the graph metrics, using the Anatomic-Automatic Labelling (AAL) parcellation scheme. We quantified the reliability of the graph metrics computed both at global and regional level depending, at optimal cost, on two key parameters, the sample size and the number of time points or scan duration. In the cost range between 20% to 35%, most of the global graph metrics are reliable with 40 subjects or more with long scan duration (14min 24s). In large samples (for instance, 100 subjects), most global and regional graph metrics are reliable for a minimum scan duration of 7min 14s. Finally, for 40 subjects and long scan duration (14min 24s), the reliable regions are located in the main areas of the default mode network (DMN), the motor and the visual networks.