current_centr: Find current-flow closeness centrality for a single graph

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

Description

A variant of closeness centrality based on circuits

Usage

current_centr(graph)

Arguments

graph

An igraph object or correlation matrix

Details

Current flow centrality was developed based on the properties of electrical circuits. It is a variant of closeness centrality that imagines edges resistors and the nodes as relays between resistors. Weighted edge information is taken into account as the absolute value. Non-zero edge are conceptually "conductors" while zero edges are "resistors."

Current flow centrality is somewhat mathematically involved, but the final formula is

\displaystyle{∑_j A_{i,j} (v_{i}^{(s,t)} - v_{j}^{(s,t)}) = u_{i}^{(s,t)}}$.

See the website in the references for a full explanation. The method involves calculating the laplacian representation of a graph. This code is modified from the code in the centiserve package.

Value

A numeric vector contaning the centrality scores for the selected vertices.

Author(s)

Brandon Vaughan

Mahdi Jalili

References

Brandes U., Fleischer D. (2005) Centrality Measures Based on Current Flow. In: Diekert V., Durand B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg

https://www.sci.unich.it/~francesc/teaching/network/flowcentrality.html

See Also

closeness_centr laplace_centr

Examples

current_centr(graph)

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