Conditional uniform graph test

Compares a statistic of the observed network with its distribution in random networks that share some of its features (Anderson, Butts and Carley, 1999; Wasserman and Faust, 1994).

Usage

cug_test(
  A,
  FUN,
  cmode = c("edges", "size", "dyad"),
  reps = 1000,
  digraph = TRUE,
  ...
)

Arguments

A

A square matrix

FUN

A function that takes a matrix and returns a single number

cmode

The feature that the random networks share with the observed one: size, edges (default) or dyad

reps

Number of random networks

digraph

Whether the matrix is directed or undirected

...

Other arguments passed to FUN

Value

This function returns the observed statistic, the mean and the standard deviation of the distribution, and the proportion of random networks with a statistic greater or equal, and lower or equal, than the observed one.

Details

The random networks are drawn from a uniform distribution conditioned on:

size: only the number of nodes, so every tie is present with probability one half,

edges: the number of nodes and the number of ties,

dyad: the dyad census, i.e. the number of mutual, asymmetric and null dyads (U|MAN).

The test says whether the statistic is higher or lower than expected once those features are taken into account. Conditioning on the dyad census, for instance, removes the tendency towards reciprocity before looking at the triads.

References

Anderson, B. S., Butts, C. and Carley, K. (1999). The interaction of size and density with graph-level indices. Social Networks, 21(3), 239–267. doi:10.1016/S0378-8733(99)00011-8

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, 1, 0, 0, 0,
  1, 0, 1, 0, 0, 0,
  1, 1, 0, 1, 0, 0,
  0, 0, 1, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  0, 0, 0, 1, 1, 0
), byrow = TRUE, ncol = 6)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

set.seed(18051889)
cug_test(A,
  FUN = function(x) trans_coef(x, method = "global"),
  cmode = "edges", reps = 100, digraph = FALSE
)
#> $observed
#> [1] 0.6
#> 
#> $mean
#> [1] 0.3826693
#> 
#> $sd
#> [1] 0.1999829
#> 
#> $p_greater
#> [1] 0.14
#> 
#> $p_lower
#> [1] 0.87
#> 
#> $distribution
#>   [1] 0.2500000 0.2727273 0.6428571 0.3000000 0.4615385 0.5000000 0.5000000
#>   [8] 0.4615385 0.4615385 0.5000000 0.4615385 0.2727273 0.2727273 0.2727273
#>  [15] 0.0000000 0.4000000 0.4615385 0.2727273 0.0000000 0.4615385 0.3000000
#>  [22] 0.5000000 0.5000000 0.5000000 0.2727273 0.2500000 0.2500000 0.4615385
#>  [29] 0.4285714 0.8000000 0.2727273 0.0000000 0.6428571 0.2727273 0.0000000
#>  [36] 0.2727273 0.2500000 0.0000000 0.6428571 0.4615385 0.6428571 0.4615385
#>  [43] 0.4615385 0.3000000 0.8000000 0.5454545 0.8000000 0.2727273 1.0000000
#>  [50] 0.4615385 0.5000000 0.2500000 0.2727273 0.6000000 0.4615385 0.4615385
#>  [57] 0.2727273 0.6428571 0.5000000 0.2727273 0.4285714 0.5000000 0.5000000
#>  [64] 0.5454545 0.4000000 0.4615385 0.4000000 0.2727273 0.5000000 0.5000000
#>  [71] 0.8000000 0.2727273 0.2500000 0.4285714 0.2727273 0.2727273 0.0000000
#>  [78] 0.0000000 0.2500000 0.3000000 0.2727273 0.6428571 0.0000000 0.2727273
#>  [85] 0.2500000 0.5000000 0.2727273 0.4285714 0.4615385 0.6428571 0.2727273
#>  [92] 0.0000000 0.2727273 0.2500000 0.2500000 0.0000000 0.6428571 0.4615385
#>  [99] 0.2727273 0.4615385
#> 
#> $cmode
#> [1] "edges"
#>