The Ubiquity of Small-World Networks

Telesford, Qawi K.; Joyce, Karen E.; Hayasaka, Satoru; Burdette, Jonathan H.; Laurienti, Paul J.

doi:10.1089/brain.2011.0038

Cited by 399 publications

(401 citation statements)

References 30 publications

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“…A network with large C and small L is often characterized as a small-world network (Watts and Strogatz, 1998), simultaneously supporting local specializations and efficient global communication (Bullmore and Sporns, 2009;Rubinov and Sporns, 2010;Telesford et al, 2011a). Both C and L have been closely examined in the brain network literature, and brain networks, both anatomical and functional, have been found to be small-world networks (Bullmore and Sporns, 2009;Humphries and Gurney, 2008;Telesford et al, 2011b). To compare C and L between the LinCorr and XSampEnt networks, normalized clustering coefficient and path length were also calculated.…”

Section: Methodsmentioning

confidence: 99%

Functional Brain Networks Formed Using Cross-Sample Entropy Are Scale Free

et al. 2014

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Over the previous decade, there has been an explosion of interest in network science, in general, and its application to the human brain, in particular. Most brain network investigations to date have used linear correlations (LinCorr) between brain areas to construct and then interpret brain networks. In this study, we applied an entropy-based method to establish functional connectivity between brain areas. This method is sensitive to both nonlinear and linear associations. The LinCorr-based and entropy-based techniques were applied to resting-state functional magnetic resonance imaging data from 10 subjects, and the resulting networks were compared. The networks derived from the entropy-based method exhibited power-law degree distributions. Moreover, the entropybased networks had a higher clustering coefficient and a shorter path length compared with that of the LinCorr-based networks. While the LinCorr-based networks were assortative, with nodes with similar degrees preferentially connected, the entropy-based networks were disassortative, with high-degree hubs directly connected to low-degree nodes. It is likely that the differences in clustering and assortativity are due to ''megahubs'' in the entropy-based networks. These mega-hubs connect to a large majority of the nodes in the network. This is the first work clearly demonstrating differences between functional brain networks using linear and nonlinear techniques. The key finding is that the nonlinear technique produced networks with scale-free degree distributions. There remains debate among the neuroscience community as to whether human brains are scale free. These data support the argument that at least some aspects of the human brain are perhaps scale free.

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Section: Methodsmentioning

confidence: 99%

Functional Brain Networks Formed Using Cross-Sample Entropy Are Scale Free

et al. 2014

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“…However, one should probably not look at the path length itself but at the relative path length, which is defined as the average path length of a given network divided by the average path length of a random network of the same size and average degree. Normalizing networks' characteristics by those of the corresponding random graphs is a procedure usually used to compare networks of different sizes [36,37,38]. Thus, we will use the relative path length to describe the networks under consideration and to compare them.…”

Section: Resultsmentioning

confidence: 99%

Mapping the q-voter model: From a single chain to complex networks

Jędrzejewski

Sznajd-Weron

Szwabiński

2016

Physica A: Statistical Mechanics and its Applications

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We propose and compare six different ways of mapping the modified q-voter model to complex networks. Considering square lattices, Barabási-Albert, Watts-Strogatz and real Twitter networks, we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level. Using Monte Carlo simulations we show that the answer depends on the relative average path length of the network and for real-life topologies the differences between the considered mappings may be negligible.

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“…These characteristics (Wasserman and Faust, 1994) result in networks with unique properties of regional specialization with efficient and global integration (Telesford et al, 2011), (Giuliani and Pietrobelli, 2014). According to Watts and Strogatz, (1998), a small-world network is ''a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps.…”

Section: Social Network Analysismentioning

confidence: 99%