Clinical Issues—August 2022

Wright, Renae

doi:10.1002/aorn.13750

Cited by 1 publication

(2 citation statements)

References 7 publications

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“…The pseudospectrum of a matrix A with eigenspectrum σ ( A ) is defined as σϵfalse(Afalse)=falsefalse{σfalse(A+Efalse) : falsefalse‖Efalsefalse‖≤ϵfalsefalse},for some ϵ>0 and E a matrix of norm less than ϵ. It measures how the spectrum changes subject to perturbations, and can be computed using the Julia package [69] based on EigTool [70]. The pseudospectra have recently been shown to be important in complex networks and the stability of ecosystems [71].…”

Section: Influence and Influenceability Of Structurementioning

confidence: 99%

“…The pseudospectrum of a matrix A with eigenspectrum σ ( A ) is defined as

for some

0

and E a matrix of norm less than

. It measures how the spectrum changes subject to perturbations, and can be computed using the Julia package [ 69 ] based on EigTool [ 70 ]. The pseudospectra have recently been shown to be important in complex networks and the stability of ecosystems [ 71 ].…”

Section: Influence and Influenceability Of Structurementioning

confidence: 99%

See 1 more Smart Citation

Influence and influenceability: global directionality in directed complex networks

Rodgers,

Tiňo,

Johnson

2023

R. Soc. open sci.

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Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of trophic analysis to study directed networks and show that both ‘influence’ and ‘influenceability’ in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localizes; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalized rock–paper–scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted—that node hierarchy is essential for understanding network influence, mediated by global directionality—are applicable to many real-world dynamics.

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