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.

We investigated large-scale systems organization of the whole human brain using functional magnetic resonance imaging (fMRI) data acquired from healthy volunteers in a no-task or 'resting' state. Images were parcellated using a prior anatomical template, yielding regional mean time series for each of 90 regions (major cortical gyri and subcortical nuclei) in each subject. Significant pairwise functional connections, defined by the group mean inter-regional partial correlation matrix, were mostly either local and intrahemispheric or symmetrically interhemispheric. Low-frequency components in the time series subtended stronger inter-regional correlations than high-frequency components. Intrahemispheric connectivity was generally related to anatomical distance by an inverse square law; many symmetrical interhemispheric connections were stronger than predicted by the anatomical distance between bilaterally homologous regions. Strong interhemispheric connectivity was notably absent in data acquired from a single patient, minimally conscious following a brainstem lesion. Multivariate analysis by hierarchical clustering and multidimensional scaling consistently defined six major systems in healthy volunteers-- corresponding approximately to four neocortical lobes, medial temporal lobe and subcortical nuclei- - that could be further decomposed into anatomically and functionally plausible subsystems, e.g. dorsal and ventral divisions of occipital cortex. An undirected graph derived by thresholding the healthy group mean partial correlation matrix demonstrated local clustering or cliquishness of connectivity and short mean path length compatible with prior data on small world characteristics of non-human cortical anatomy. Functional MRI demonstrates a neurophysiological architecture of the normal human brain that is anatomically sensible, strongly symmetrical, disrupted by acute brain injury, subtended predominantly by low frequencies and consistent with a small world network topology.

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We explored properties of whole brain networks based on multivariate spectral analysis of human functional magnetic resonance imaging (fMRI) time-series measured in 90 cortical and subcortical subregions in each of five healthy volunteers studied in the (no-task) resting state. We note that undirected graphs representing conditional independence between multivariate time-series can be more readily approached in the frequency domain than the time domain. Estimators of partial coherency and normalized partial mutual information f, an integrated measure of partial coherence over an arbitrary frequency band, are applied. Using these tools, we replicate the prior observations that bilaterally homologous brain regions tend to be strongly connected and functional connectivity is generally greater at low frequencies [0.0004, 0.1518 Hz]. We also show that long-distance intrahemispheric connections between regions of prefrontal and parietal cortex were more salient at low frequencies than at frequencies greater than 0.3 Hz, whereas many local or short-distance connections, such as those comprising segregated dorsal and ventral paths in posterior cortex, were also represented in the graph of high-frequency connectivity. We conclude that the partial coherency spectrum between a pair of human brain regional fMRI time-series depends on the anatomical distance between regions: long-distance (greater than 7 cm) edges represent conditional dependence between bilaterally symmetric neocortical regions, and between regions of prefrontal and parietal association cortex in the same hemisphere, are predominantly subtended by low-frequency components.