Is the brain really a small-world network?
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ABSTRACT:
SUBMITTER: Hilgetag CC
PROVIDER: S-EPMC4853440 | biostudies-literature | 2016 May
REPOSITORIES: biostudies-literature
Publications
Is the brain really a small-world network?
Hilgetag Claus C CC Goulas Alexandros A
Brain structure & function 20150418 4
Similar Datasets
Project description:Aberrant topological properties of small-world human brain networks in patients with schizophrenia (SZ) have been documented in previous neuroimaging studies. Aberrant functional network connectivity (FNC, temporal relationships among independent component time courses) has also been found in SZ by a previous resting state functional magnetic resonance imaging (fMRI) study. However, no study has yet determined if topological properties of FNC are also altered in SZ. In this study, small-world network metrics of FNC during the resting state were examined in both healthy controls (HCs) and SZ subjects. FMRI data were obtained from 19 HCs and 19 SZ. Brain images were decomposed into independent components (ICs) by group independent component analysis (ICA). FNC maps were constructed via a partial correlation analysis of ICA time courses. A set of undirected graphs were built by thresholding the FNC maps and the small-world network metrics of these maps were evaluated. Our results demonstrated significantly altered topological properties of FNC in SZ relative to controls. In addition, topological measures of many ICs involving frontal, parietal, occipital and cerebellar areas were altered in SZ relative to controls. Specifically, topological measures of whole network and specific components in SZ were correlated with scores on the negative symptom scale of the Positive and Negative Symptom Scale (PANSS). These findings suggest that aberrant architecture of small-world brain topology in SZ consists of ICA temporally coherent brain networks.
| S-EPMC3182226 | biostudies-literature
Project description:Quantitative descriptions of network structure can provide fundamental insights into the function of interconnected complex systems. Small-world structure, diagnosed by high local clustering yet short average path length between any two nodes, promotes information flow in coupled systems, a key function that can differ across conditions or between groups. However, current techniques to quantify small-worldness are density dependent and neglect important features such as the strength of network connections, limiting their application in real-world systems. Here, we address both limitations with a novel metric called the Small-World Propensity (SWP). In its binary instantiation, the SWP provides an unbiased assessment of small-world structure in networks of varying densities. We extend this concept to the case of weighted brain networks by developing (i) a standardized procedure for generating weighted small-world networks, (ii) a weighted extension of the SWP, and (iii) a method for mapping observed brain network data onto the theoretical model. In applying these techniques to compare real-world brain networks, we uncover the surprising fact that the canonical biological small-world network, the C. elegans neuronal network, has strikingly low SWP. These metrics, models, and maps form a coherent toolbox for the assessment and comparison of architectural properties in brain networks.
| S-EPMC4766852 | biostudies-other
Project description:To investigate the topological properties of the functional connectivity and their relationships with cognition impairment in subcortical vascular cognitive impairment (SVCI) patients, resting-state fMRI and graph theory approaches were employed in 23 SVCI patients and 20 healthy controls. Functional connectivity between 90 brain regions was estimated using bivariate correlation analysis and thresholded to construct a set of undirected graphs. Moreover, all of them were subjected to a battery of cognitive assessment, and the correlations between graph metrics and cognitive performance were further analyzed. Our results are as follows: functional brain networks of both SVCI patients and controls showed small-world attributes over a range of thresholds(0.15?sparsity?0.40). However, global topological organization of the functional brain networks in SVCI was significantly disrupted, as indicated by reduced global and local efficiency, clustering coefficients and increased characteristic path lengths relative to normal subjects. The decreased activity areas in SVCI predominantly targeted in the frontal-temporal lobes, while subcortical regions showed increased topological properties, which are suspected to compensate for the inefficiency of the functional network. We also demonstrated that altered brain network properties in SVCI are closely correlated with general cognitive and praxis dysfunction. The disruption of whole-brain topological organization of the functional connectome provides insight into the functional changes in the human brain in SVCI.
| S-EPMC4489389 | biostudies-literature
Project description:Graph theory deterministically models networks as sets of vertices, which are linked by connections. Such mathematical representation of networks, called graphs are increasingly used in neuroscience to model functional brain networks. It was shown that many forms of structural and functional brain networks have small-world characteristics, thus, constitute networks of dense local and highly effective distal information processing. Motivated by a previous small-world connectivity analysis of resting EEG-data we explored implications of a commonly used analysis approach. This common course of analysis is to compare small-world characteristics between two groups using classical inferential statistics. This however, becomes problematic when using measures of inter-subject correlations, as it is the case in commonly used brain imaging methods such as structural and diffusion tensor imaging with the exception of fibre tracking. Since for each voxel, or region there is only one data point, a measure of connectivity can only be computed for a group. To empirically determine an adequate small-world network threshold and to generate the necessary distribution of measures for classical inferential statistics, samples are generated by thresholding the networks on the group level over a range of thresholds. We believe that there are mainly two problems with this approach. First, the number of thresholded networks is arbitrary. Second, the obtained thresholded networks are not independent samples. Both issues become problematic when using commonly applied parametric statistical tests. Here, we demonstrate potential consequences of the number of thresholds and non-independency of samples in two examples (using artificial data and EEG data). Consequently alternative approaches are presented, which overcome these methodological issues.
| S-EPMC3536769 | biostudies-other
Project description:Protest diffusion is a cascade process that can spread over different regions of the planet. The way and the extension that this phenomenon can occur is still not properly understood. Here, we empirically investigate this question using protest data from GDELT and ICEWS, two of the most extensive and longest-running data sets freely available. We divide the globe into grid cells and construct a temporal network for each data set where nodes represent cells and links are established between nodes if their protest events co-occur. We show that the temporal networks are small-world, indicating that the cells are directly linked or separated by a few steps on average. Furthermore, the average path lengths are decreasing through the years, which suggests that the world is becoming "smaller". The persistent temporal hubs present in both data sets indicate that protests can spread faster through the hubs. This topological feature is consistent with the hypothesis that protests can quickly diffuse from one region to any other part of the globe.
| S-EPMC8479126 | biostudies-literature
Project description:ObjectiveWe test the hypothesis that brain networks associated with cognitive function shift away from a "small-world" organization following traumatic brain injury (TBI).MethodsWe investigated 20 TBI patients and 21 age-matched controls. Resting-state functional MRI was used to study functional connectivity. Graph theoretical analysis was then applied to partial correlation matrices derived from these data. The presence of white matter damage was quantified using diffusion tensor imaging.ResultsPatients showed characteristic cognitive impairments as well as evidence of damage to white matter tracts. Compared to controls, the graph analysis showed reduced overall connectivity, longer average path lengths, and reduced network efficiency. A particular impact of TBI is seen on a major network hub, the posterior cingulate cortex. Taken together, these results confirm that a network critical to cognitive function shows a shift away from small-world characteristics.ConclusionsWe provide evidence that key brain networks involved in supporting cognitive function become less small-world in their organization after TBI. This is likely to be the result of diffuse white matter damage, and may be an important factor in producing cognitive impairment after TBI.
| S-EPMC3908350 | biostudies-literature
Project description:Continuous deterministic models have been widely used to guide non-pharmaceutical interventions (NPIs) to combat the spread of the coronavirus disease 2019 (COVID-19). The validity of continuous deterministic models is questionable because they fail to incorporate two important characteristics of human society: high clustering and low degree of separation. A small-world network model is used to study the spread of COVID-19, thus providing more reliable information to provide guidance to mitigate it. Optimal timing of lockdown and reopening society is investigated so that intervention measures to combat COVID-19 can work more efficiently. Several important findings are listed as follows: travel restrictions should be implemented as soon as possible; if 'flattening the curve' is the purpose of the interventions, measures to reduce community transmission need not be very strict so that the lockdown can be sustainable; the fraction of the population that is susceptible, rather than the levels of daily new cases and deaths, is a better criterion to decide when to reopen society; and society can be safely reopened when the susceptible population is still as high as 70%, given that the basic reproduction number is 2.5. Results from small-world network models can be significantly different than those from continuous deterministic models, and the differences are mainly due to a major shortfall intrinsically embedded in the continuous deterministic models. As such, small-world network models provide meaningful improvements over continuous deterministic models and therefore should be used in the mathematical modeling of infection spread to guide the present COVID-19 interventions. For future epidemics, the present framework of mathematical modeling can be a better alternative to continuous deterministic models.
| S-EPMC8516975 | biostudies-literature
Project description:Resting-state functional magnetic resonance imaging (fMRI) with graph theoretical modeling has been increasingly applied for assessing whole brain network topological organization, yet its reproducibility remains controversial. In this study, we acquired three repeated resting-state fMRI scans from 16 healthy controls during a strictly controlled in-laboratory study and examined the test-retest reliability of seven global and three nodal brain network metrics using different data processing and modeling strategies. Among the global network metrics, the characteristic path length exhibited the highest reliability, whereas the network small-worldness performed the poorest. Nodal efficiency was the most reliable nodal metric, whereas betweenness centrality showed the lowest reliability. Weighted global network metrics provided better reliability than binary metrics, and reliability from the AAL90 atlas outweighed those from the Power264 parcellation. Although global signal regression had no consistent effects on the reliability of global network metrics, it slightly impaired the reliability of nodal metrics. These findings provide important implications for the future utility of graph theoretical modeling in brain network analyses.
| S-EPMC10216465 | biostudies-literature
Project description:Most previous imaging studies have used traditional Pearson correlation analysis to construct brain networks. This approach fails to adequately and completely account for the interaction between adjacent brain regions. In this study, we used the L1-norm linear regression model to test the small-world attributes of the brain networks of three groups of patients, namely, those with mild cognitive impairment (MCI), Alzheimer's disease (AD), and healthy controls (HCs); we attempted to identify the method that may detect minor differences in MCI and AD patients. Twenty-four AD patients, 33 MCI patients, and 27 HC elderly subjects were subjected to functional MRI (fMRI). We applied traditional Pearson correlation and the L1-norm to construct the brain networks and then tested the small-world attributes by calculating the following parameters: clustering coefficient (Cp), path length (Lp), global efficiency (Eg), and local efficiency (Eloc). As expected, L1 could detect slight changes, mainly in MCI patients expressing higher Cp and Eloc; however, no statistical differences were found between MCI patients and HCs in terms of Cp, Lp, Eg, and Eloc, using Pearson correlation. Compared with HCs, AD patients expressed a lower Cp, Eloc, and Lp and an increased Eg using both connectivity metrics. The statistical differences between the groups indicated the brain networks constructed by the L1-norm were more sensitive to detect slight small-world network changes in early stages of AD.
| S-EPMC7351016 | biostudies-literature
Project description:BackgroundMany technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model--the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified.Methodology/principal findingsWe defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S>1--an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process.Conclusions/significanceWe have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing.
| S-EPMC2323569 | biostudies-literature