hubbell: Find the Hubbell centrality or the Hubbell Index

In centiserve: Find Graph Centrality Indices

Description

Hubbell centrality defined as:

C(h) = E + WC(h)

where E is some exogeneous input and w is a weight matrix derived from the adjancancy matrix A.

Usage

hubbell(graph, vids = V(graph), weights = NULL, weightfactor = 0.5)

Arguments

graph	The input graph as igraph object
vids	Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices.
weights	Possibly a numeric vector giving edge weights. If this is NULL, the default, and the graph has a weight edge attribute, then the attribute is used. If this is NA then no weights are used (even if the graph has a weight attribute).
weightfactor	The weight factorLogical which must be greater than 0. The defualt is 0.5.

Details

This centrality value is defined by means of a weighted and loop allowed network. The weighted adjacency matrix w of a network G is asymmetric and contains real-valued weights for each edge.
More detail at Hubbell Index

Value

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

Author(s)

Mahdi Jalili [e-mail]

Algorithm adapted from CentiLib (Grabler, Johannes, 2012).

References

Hubbell, Charles H. "An input-output approach to clique identification." Sociometry (1965): 377-399.

Grabler, Johannes, Dirk Koschutzki, and Falk Schreiber. "CentiLib: comprehensive analysis and exploration of network centralities." Bioinformatics 28.8 (2012): 1178-1179.

Examples

g <- barabasi.game(100)
hubbell(g)

Example output

Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: Matrix
  [1] 1.000000 1.500000 1.750000 1.500000 1.500000 1.500000 1.750000 1.750000
  [9] 1.500000 1.875000 1.500000 1.750000 1.500000 1.750000 1.750000 1.500000
 [17] 1.875000 1.750000 1.875000 1.937500 1.937500 1.750000 1.875000 1.875000
 [25] 1.875000 1.937500 1.968750 1.750000 1.750000 1.875000 1.750000 1.750000
 [33] 1.750000 1.937500 1.750000 1.875000 1.750000 1.937500 1.875000 1.500000
 [41] 1.875000 1.750000 1.750000 1.500000 1.500000 1.937500 1.875000 1.750000
 [49] 1.750000 1.500000 1.937500 1.500000 1.937500 1.875000 1.750000 1.500000
 [57] 1.750000 1.750000 1.750000 1.937500 1.500000 1.750000 1.984375 1.875000
 [65] 1.750000 1.750000 1.750000 1.750000 1.500000 1.968750 1.750000 1.937500
 [73] 1.875000 1.750000 1.937500 1.750000 1.875000 1.750000 1.937500 1.875000
 [81] 1.937500 1.750000 1.500000 1.968750 1.750000 1.750000 1.750000 1.968750
 [89] 1.875000 1.750000 1.937500 1.750000 1.875000 1.875000 1.937500 1.500000
 [97] 1.875000 1.875000 1.937500 1.937500

centiserve documentation built on May 2, 2019, 6:01 a.m.