The complex hierarchical topology of EEG functional connectivity

Smith, Keith; Escudero, Javier

doi:10.1016/j.jneumeth.2016.11.003

Cited by 21 publications

(40 citation statements)

References 50 publications

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“…where D is the number of distinct degrees in the network and µ p (j) is the mean of the jth entries of all p length neighbourhood degree sequences [47]. For the tier-based analyses, we used degree specific HC by averaging it over a given range of degrees, i.e.…”

Section: Hierarchical Complexitymentioning

confidence: 99%

Hierarchical complexity of the macro-scale neonatal brain

Blesa

Galdi

Cox³

et al. 2020

Preprint

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The human adult structural connectome has a rich topology composed of nodal hierarchies containing highly diverse connectivity patterns, aligned to the diverse range of functional specialisations in the brain. The emergence of this hierarchical complexity in human development is unknown. Here, we substantiate the hierarchical tiers and complexity of brain networks in the newborn period, assess correspondences with hierarchical complexity in adulthood, and investigate the effect of preterm birth, a leading cause of neurocognitive impairment and atypical brain development, on hierarchical complexity. We report that the neonatal and adult structural connectomes are both composed of distinct hierarchical tiers. Consistency of ROIs is found at both ends of this hierarchy during early life and in adulthood, but significant differences are evident in intermediate tiers. The neonatal connectome is hierarchically complex in term born neonates, but hierarchically complexity is altered in association with preterm birth. This is mainly due to diversity of connectivity patterns in Tier 3, which is comprised of regions that underlie sensorimotor processing and its integration with cognitive information. For neonates and adults, the highest tier (comprising hub regions) is ordered, rather than complex, with more homogeneous connectivity patterns in structural hubs. This suggests that the brain develops first a more rigid hierarchical structure in hub regions allowing for the development of greater and more diverse functional specialisation in lower level regions, while connectivity underpinning this diversity is dysmature in infants born preterm.

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Section: Hierarchical Complexitymentioning

confidence: 99%

Hierarchical complexity of the macro-scale neonatal brain

Blesa

Galdi

Cox³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…where is the number of distinct degrees in the network and K ( ) is the mean of the th entries of all length neighbourhood degree sequences 10 . For the tier-based analyses, we used degree specific hierarchical complexity by averaging hierarchical complexity over a given range of degrees, i.e.…”

Section: Hierarchical Complexitymentioning

confidence: 99%

“…However, it has yet to be determined whether dissimilarity of connectivity patterns is itself a feature which can advance our understanding of brain structure. Just such a feature can be extracted using the recently developed hierarchical complexity paradigm 10,11 .…”

Section: Introductionmentioning

confidence: 99%

“…This includes a detailed analysis of complexity within the hierarchical levels of these connectomes. This recently introduced paradigm has been validated only in an electroencephalogram (EEG) functional connectivity study 10 . It posits that network complexity is characterised by nodes of the same degree (hierarchically equivalent nodes) being connected in highly variable ways with respect to the degrees of nodes they connect to (having highly variable connectivity patterns), as illustrated in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…This concerns wholly separate considerations of topology to the well-known paradigms of small-world 12 and scale-free 13 complex networks-the former stemming from the idea that there are no more than six degrees of separation between any two people, which is exhibited with network characteristics of high clustering and low shortest path lengths, and the latter being that complex networks display power-law degree distributions, crudely identifiable by having few hub nodes with many connections and many peripheral nodes with few connections. Similarly, in seeking to define the notion of complexity, it takes a different stance to the standard notion of complexity arising between random and ordered systems 14 , instead proposing that both such systems have inherently more predictable connectivity patterns than real-world complex networks 10 .…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Complexity of the Adult Human Structural Connectome

Smith

Bastin

Cox

et al. 2018

Preprint

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Normalised degree variance

Smith

Escudero

2020

Appl Netw Sci

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Finding graph indices which are unbiased to network size and density is of high importance both within a given field and across fields for enhancing comparability of modern network science studies. The degree variance is an important metric for characterising network degree heterogeneity. Here, we provide an analytically valid normalisation of degree variance to replace previous normalisations which are either invalid or not applicable to all networks. It is shown that this normalisation provides equal values for graphs and their complements; it is maximal in the star graph (and its complement); and its expected value is constant with respect to density for Erdös-Rényi (ER) random graphs of the same size. We strengthen these results with model observations in ER random graphs, random geometric graphs, scale-free networks, random hierarchy networks and resting-state brain networks, showing that the proposed normalisation is generally less affected by both network size and density than previous normalisation attempts. The closed form expression proposed also benefits from high computational efficiency and straightforward mathematical analysis. Analysis of 184 real-world binary networks across different disciplines shows that normalised degree variance is not correlated with average degree and is robust to node and edge subsampling. Comparisons across subdomains of biological networks reveals greater degree heterogeneity among brain connectomes and food webs than in protein interaction networks.

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The complex hierarchical topology of EEG functional connectivity

Abstract: Our metric and model provide a rigorous characterisation of hierarchical complexity. Importantly, our framework shows a scale of complexity arising between 'all nodes are equal' topologies at one extreme and 'strict class-based' topologies at the other.

Cited by 21 publications

References 50 publications

Hierarchical complexity of the macro-scale neonatal brain

Hierarchical complexity of the macro-scale neonatal brain

Hierarchical Complexity of the Adult Human Structural Connectome

Normalised degree variance

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