delta_energy: Calculate the nodewise-deletion change in graph energy for a...

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

Description

This function calculates the change in graph energy observed due to the deletion of each node in the graph.

Usage

delta_energy(graph)

Arguments

graph

A network as an igraph object

Details

Fornito, Zalesky, and Bullmore define a delta centrality measure as one that measures the change in a global property of the graph that occurs due to the deletion of a node or edge (Fornito et al, 2016). One informative global property is the energy of a graph. 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. Therefore, to understand the importance of a particular node to the connectivity of the graph a node can be removed and the change in graph energy used as a measure of node importance.

Value

A vector of centrality scores for each node.

Author(s)

Brandon Vaughan

References

Fornito, A., Zalesky, A., & Bullmore, E. (2016). Centrality and Hubs. Chapter 5. Fundamentals of Brain Network Analysis, 137-161. doi:10.1016/b978-0-12-407908-3.00005-4

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

See Also

laplace_centr graph_energy fiedler_value

Examples

delta_e = delta_energy(Graph)

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