I try to compare the output of local transitivity and Barrat transitivity using igragh. However, I have problems with how they are calculated for directed graph. The result seems different from what I expected.

When calculate local transitivity, the direction is ignored. I calculated the local transitivity by number of closed triads devided by all possible triads (refer to Wasserman & Faust, 1994). But the result is 0.1666667 NaN NaN 1 1, same as the output of Barrat transitivity. Can anyone kindly explain it? Thanks a lot!

Below are the codes and output.

```
< g_1 <- graph( edges=c(1,2,1,3,1,4,1,5,4,1,5,1,4,5), n=5, directed=T)
< transitivity(g_1, type="local", isolates = "NaN")
#[1] 0.06666667 NaN NaN 0.33333333 0.33333333
< transitivity(g_1, type="Barrat", isolates = "NaN")
#[1] 0.1666667 NaN NaN 1.0000000 1.0000000
```