rigraphtransitivity

Inconsistent Local Transitivity Output in igraph

I need to determine the transitivity for each node in a network, but am getting inconsistent results.

set.seed(123)    
a <- rbinom(144, 1, .5)
b <- graph.adjacency(matrix(a, nrow = 12, ncol = 12), mode = "undirected")

transitivity(b, type = "local")

This provides the output:

 [1] 0.6888889 0.4909091 0.4444444 0.9333333 0.4909091 0.7500000 0.7333333 0.4666667 0.7333333 0.4222222 0.5000000
[12] 0.6944444

But when I try to specify a single node, some values in the output do not match:

transitivity(b, vids = 2, type = "local")

[1] 0.75

In fact, when I try to calculate the local transitivity for all vertices, many are different than if I leave the vids argument out. In some instances when I've tried this, all have been different.

transitivity(b, vids = V(b), type = "local")

  [1] 0.6888889 0.7500000 0.7142857 0.9333333 0.7500000 0.7500000 0.7333333 0.7500000 0.7333333 0.6785714 0.8571429
[12] 0.6944444

If I set vids as NULL it matches the first output, without the vids argument included at all.

The results are slightly different, but still don't match if I create a directed network.

Any thoughts on what might be causing this or which set of results should I use?

Thank you for your help.

Solution

  • You should be aware of that your graph b is NOT a simple graph, since it contains self loops

    enter image description here

    When running transitivity over such kind of graph, you will see a warning/error message

    Transitivity works on simple graphs only. The result might be incorrect. igraph 1.3.0 and later will treat this as an error.

    Thus, if you would like to use transitivity in a correct manner, you should exclude self loops first, e.g.,

    b <- simplify(graph.adjacency(matrix(a, nrow = 12, ncol = 12), mode = "undirected"))

    and then you will see

    > transitivity(b, type = "local")
 [1] 0.6888889 0.7500000 0.7142857 0.9333333 0.7500000 0.7500000 0.7333333
 [8] 0.7500000 0.7333333 0.6785714 0.8571429 0.6944444

> transitivity(b, vids = V(b), type = "local")
 [1] 0.6888889 0.7500000 0.7142857 0.9333333 0.7500000 0.7500000 0.7333333
 [8] 0.7500000 0.7333333 0.6785714 0.8571429 0.6944444