graph_energy: Calculate the graph energy for a single graph

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

Description

This function calculates the energy of a graph.

Usage

graph_energy(graph)

Arguments

graph

A network as an igraph object or connectivity matrix

Details

Graph energy was originally applied in organic chemistry to quantify the stability of molecular orbitals associated with pi-electrons (Li, Shi, & Gutman, 2012). The graph energy informs about the connectivity of the graph as a whole. A graph energy of zero means the nodes are not connected at all. The graph energy is calculated by summing the absolute values of the eigenvalues for the matrix. See Daianu et al (2015) for an example of an application to neuroimaging.

Value

A numeric value of the graph energy

Author(s)

Brandon Vaughan

References

Daianu, M., Mezher, A., Jahanshad, N., Hibar, D. P., Nir, T. M., Jack, C. R., … Thompson, P. M. (2015). SPECTRAL GRAPH THEORY AND GRAPH ENERGY METRICS SHOW EVIDENCE FOR THE ALZHEIMER’S DISEASE DISCONNECTION SYNDROME IN APOE-4 RISK GENE CARRIERS. IEEE International Symposium on Biomedical Imaging, 2015, 458–461. http://doi.org/10.1109/ISBI.2015.7163910

Li, X.; Shi, Y.; Gutman, I. (2012), Graph Energy, New York: Springer, ISBN 978-1-4614-4219-6.

See Also

laplace_centr delta_energy fiedler_value graph_energy_mult

Examples

energy = graph_energy(Graph)

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