fiedler_value: Calculate the fiedler value for a graph

In abnormally-distributed/rsfcNet: Analyze resting state functional connectivity networks

Description

This function calculates the fiedler value for a graph.

Usage

fiedler_value(graph)

Arguments

graph

A network as an igraph object

Details

The Fiedler value is the second smallest eigenvalue of the laplacian representation of a graph. The closer the Fiedler value is to zero the more easily the graph can be split into separate components unconnected to each other. The Fiedler value is also known as the algebraic connectivity of a graph (Mohar, 1991). Hence the fiedler value can be used as a measure of a network's robustness to becoming disconnected. See Daianu et al (2014) for an application to neuroimaging.

Value

A numeric value of the fiedler value.

Author(s)

Brandon Vaughan

References

Mohar, B., The Laplacian Spectrum of Graphs, in Graph Theory, Combinatorics, and Applications, Vol. 2, Ed. Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Schwenk, Wiley, 1991, pp. 871–898.

Daianu, M., Jahanshad, N., Nir, T. M., Leonardo, C. D., Jack, C. R., Weiner, M. W., … Thompson, P. M. (2014). Algebraic connectivity of brain networks shows patterns of segregation leading to reduced network robustness in Alzheimer’s disease. Computational Diffusion MRI: MICCAI Workshop, Boston, MA, USA, September 2014. MICCAI Workshop on Computation Diffusion MRI (Boston, MA), 55–64. http://doi.org/10.1007/978-3-319-11182-7_6

See Also

laplace_centr_mult delta_energy_mult fiedler_value_mult

Examples

energy = fiedler_value(Graph)

abnormally-distributed/rsfcNet documentation built on March 8, 2020, 5:32 p.m.