Freeman degree centrality of a node, normalised

C_D(v) = deg(v) / (n - 1). The divisor is the largest degree any node can have in a simple graph on n nodes, so C_D lands in [0, 1] and is comparable across graphs of different size: the hub of a star scores exactly 1 and an isolate exactly 0. Weighted adjacency matrices are summed rather than counted.

Usage

Netdeg(A, node = 0)

Arguments

A

Adjacency or weight matrix.

node

Zero-based index of the node whose centrality is returned.

Value

List with estimate (normalised C_D), degree (raw), node, n.

References

Freeman (1979), Social Networks 1(3), 215-239, doi:10.1016/0378-8733(78)90021-7 .

Examples

A <- matrix(c(4, 1, 0.5, 1, 3, 0.8, 0.5, 0.8, 2), nrow = 3)
res <- Netdeg(A = A)
res
#> $estimate
#> [1] 0.75
#> 
#> $degree
#> [1] 1.5
#> 
#> $node
#> [1] 0
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "Freeman degree centrality (normalised)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"