Transitivity

This measure is sometimes called clustering coefficient.

Usage

trans_coef(
  A,
  method = c("weakcensus", "global", "mean", "local", "barrat"),
  select = c("all", "in", "out")
)

Arguments

A

A matrix

method

Whether to calculate the weakcensus, global transitivity ratio, the mean transitivity, the local transitivity or the weighted transitivity of barrat.

select

Whether to consider all, in or out ties for the local transitivity.

Value

Return a transitivity measure

References

Barrat, A., Barthelemy, M., Pastor-Satorras, R. and Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101(11), 3747–3752. doi:10.1073/pnas.0400087101

Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 0, 1, 0,
  1, 0, 1, 1, 0,
  0, 1, 0, 0, 0,
  1, 1, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:ncol(A)]
colnames(A) <- rownames(A)

trans_coef(A, method = "local")
#> $a
#> [1] 1
#> 
#> $b
#> [1] 0.3333333
#> 
#> $c
#> [1] NaN
#> 
#> $d
#> [1] 0.3333333
#> 
#> $e
#> [1] NaN
#> 

# The weighted transitivity of Barrat et al. (2004) weighs each triangle
# by the strength of the two ties of the node
W <- matrix(c(
  0, 4, 0, 2, 0,
  4, 0, 1, 3, 0,
  0, 1, 0, 0, 0,
  2, 3, 0, 0, 5,
  0, 0, 0, 5, 0
), byrow = TRUE, ncol = 5)
trans_coef(W, method = "barrat")
#> [1] 1.0000 0.4375     NA 0.2500     NA