Processing math: 100%
Skip to contents

Calculates a measure of diversity for all vertices.

Usage

diversity(graph, weights = NULL, vids = V(graph))

Arguments

graph

The input graph. Edge directions are ignored.

weights

NULL, or the vector of edge weights to use for the computation. If NULL, then the ‘weight’ attibute is used. Note that this measure is not defined for unweighted graphs.

vids

The vertex ids for which to calculate the measure.

Value

A numeric vector, its length is the number of vertices.

Details

The diversity of a vertex is defined as the (scaled) Shannon entropy of the weights of its incident edges: D(i)=H(i)logki and H(i)=kij=1pijlogpij, where pij=wijkil=1Vil, and ki is the (total) degree of vertex i, wij is the weight of the edge(s) between vertices i and j.

For vertices with degree less than two the function returns NaN.

References

Nathan Eagle, Michael Macy and Rob Claxton: Network Diversity and Economic Development, Science 328, 1029--1031, 2010.

Author

Gabor Csardi csardi.gabor@gmail.com

Examples


g1 <- sample_gnp(20, 2 / 20)
g2 <- sample_gnp(20, 2 / 20)
g3 <- sample_gnp(20, 5 / 20)
E(g1)$weight <- 1
E(g2)$weight <- runif(ecount(g2))
E(g3)$weight <- runif(ecount(g3))
diversity(g1)
#>  [1]   1   0   1   1   0   0   1   1 NaN   0 NaN   1   1   1   1   0   1   1   0
#> [20]   1
diversity(g2)
#>  [1] 0.0000000 0.0000000 0.9912105 0.1954131 0.2786455       NaN 0.9285801
#>  [8]       NaN 0.9562562 0.8678366 0.9145202 0.0000000 0.9606785       NaN
#> [15] 0.0000000 0.9837941 0.0000000 0.0000000 0.0000000 0.8888561
diversity(g3)
#>  [1] 0.9153007 0.9963839 0.7610137 0.9986502 0.7908580 0.6775001 0.9359162
#>  [8] 0.9681371 0.6402843 0.9446303 0.8001961 0.9568925 0.8956848 0.2837485
#> [15] 0.8343112 0.8661485 0.8991006 0.5628532 0.8944529 0.9736941