The brainstem reticular formation is a small-world, not scale-free, network

By Mark D. Humphries, Kevin N. Gurney, Tony J. Prescott. Proceedings of the Royal Society of London. Biological Sciences, 2006

625 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, Experimental and Cognitive Psychology

View Paper: https://www.semanticscholar.org/paper/13e33c91d7a63f4858129c5a5ecae9bd819714ca

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In Cognitive Neuroscience

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Citations in the corpus

Brain graphs: graphical models of the human brain connectome. (2011, background): “It has also been the basis for graphical modeling of small-world cellular networks in vertebrate brainstem (Humphries et al. 2006).”
Small-World Brain Networks Revisited (2016, methodology): “These two statistics can be combined to construct a weighted metric of small-worldness [91]: With these deﬁnitions, small-world networks will have Γ weighted > 1, Λ weighted ∼ 1 and σ weighted > 1, [6].”
Disrupted small-world networks in schizophrenia. (2008, background): “These two conditions can also be summarized into a scalar quantitative measurement, small-worldness, = / , which is typically 41 for small-world networks (Achard et al., 2006; Humphries et al., 2006; He et al., 2007).”
Graph theoretical analysis of complex networks in the brain (2007, background): “investigated whether a specific subnetwork of the brain, the brainstem reticular formation, displays a small-world like architecture [93].”
Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. (2007, neutral): “These 2 conditions can also be summarized into a simple quantitative measurement, small worldness, r = c/k > 1 (Humphries et al. 2005; Achard et al. 2006), implying that the magnitude ratio between C real p and C rand p is greater than themagnitude ratio between L p and L rand p : In this study, we ”
Cortical High-Density Counterstream Architectures (2013, background): “(C) The small-world coefficient Cp=Co Lp=Lo (33, 136) corresponding to each lattice rewiring.”
Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence (2008, methodology): “Such networks of neurons can have very low small-world-ness values for their size [16], and thus fall far from the linear S/n model discovered here.”
Hemisphere- and gender-related differences in small-world brain networks: A resting-state functional MRI study (2011, result): “Typically, a small-world network should meet the following criteria: γN1 and λ≈1(Watts and Strogatz, 1998), or σ=γ/λN1 (Humphries et al., 2006).”
Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory (2008, neutral): “Additionally, the small- worldness condition lies in satisfying that ru g k N1 (Humphries et al., 2006).”
Optimal Hierarchical Modular Topologies for Producing Limited Sustained Activation of Neural Networks (2009, positive): “The extent of a small-world organization can be characterized by the small-world coefficient SW = (C/Crand) / (L/Lrand) (Humphries et al., 2006; Humphries and Gurney, 2008).”
Mapping Human Whole-Brain Structural Networks with Diffusion MRI (2007, neutral): “The networks available and studied to date [27,28] are simply too small to judge if their node distribution is exponential, heavy tailed, or yet different.”
The Ubiquity of Small-World Networks (2011, background): “a ratio of network clustering and path length compared to its random network equivalent(Humphries et al. 2006).”
Graph analysis of the human connectome: Promise, progress, and pitfalls (2013, neutral): “An interesting remaining question concerns the value of reducing a complex network such as the brain to a small number of summary statistics such as, for example, the small-worldness index (Humphries et al., 2006).”
A Small World of Neuronal Synchrony (2008, background): “…was inferred if the 2 networks had the same average path lengths, k 1, and if the empirical network had a larger clustering coefficient than the random network, c > 1, or, equivalently, if the ratio Sw = c/k > 1 (Montoya and Sol 2002; Achard et al. 2006; Humphries et al. 2006; He et al. 2007).”