[igraph] clustering coefficient in weighted or directional graphs

[Tom Richardson]

Hi List,

I am interested in assessing the (global) clustering coefficient in my graphs. However, as my edges are directed and weighted (though not all edges are connected to all others), the igraph function ('transitivity') for estimating the CC doesn't account for the directionality or the edge weighting.

I notice that equation 5 in  Barrat et al (2004)* gives a clustering coefficient for *weighted* (undirected) networks. 

In Newman (2010)** he states (p201) "It is possible to generalize transitivity to take account of directed links. If we have a directed relation between vertices such as "U likes V' then we can say that a triple of vertices is closed or transitive if U likes V, V likes W, and U also likes W. (Note that there are many distinct ways for such a triple to be transitive, depending on the directions of the edges. The example given here is only one of six different possibilities). One can calculate a clustering coefficient or fraction of transitive triples in the obvious fashion for the directed case, counting all directed paths of length two that are closed, and dividing by the total number of directed paths of length two. For some reason, however, such measures have not often appeared in the literature"

So, my questions are;

- In igraph, how would one implement the weighted CC  (equation 5 in Barratt 2004)?

- In igraph, how would one implement the directed CC suggested by Newman 2010?

- Would it be possible to combine the two?

I Apologies if parts of the above seem elementary, but i prefer to get good advice before embarking on a dodgy hack of my own.

Thanks!

Tom

*  Barrat et al. 2004. The architecture of complex weighted networks. PNAS. 101

** Newman, M. 2010. Networks. An Introduction.