graph.diversity

Graph diversity

Calculates a measure of diversity for all vertices.

Usage

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

Details

The diversity of a vertex is defined as the (scaled) Shannon entropy of the weights of its incident edges: $$D(i)=\frac{H(i)}{\log k_i}$$ and $$H(i)=-\sum_{j=1}^{k_i} p_{ij}\log p_{ij},$$ where $$p_{ij}=\frac{w_{ij}}{\sum_{l=1}^{k_i}}V_{il},$$ and $k_i$ is the (total) degree of vertex $i$, $w_{ij}$ is the weight of the edge(s) between vertices $i$ and $j$.

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

concept

Entropy

References

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

Aliases

• graph.diversity

Examples

g1 <- erdos.renyi.game(20, 2/20)
g2 <- erdos.renyi.game(20, 2/20)
g3 <- erdos.renyi.game(20, 5/20)
E(g1)$weight <- 1
E(g2)$weight <- runif(ecount(g2))
E(g3)$weight <- runif(ecount(g3))
graph.diversity(g1)
graph.diversity(g2)
graph.diversity(g3)