[igraph] Creation of a plot showing clustering coefficient depending on degree k

[Delphine Faugaret]

Hello,

I would like to create a graph in order to see the clustering coeffcient C(k) depending on k.

I've the following formula:

C(i)=ei/(ki(ki-1)/2) and C(k)=(1/Nk) somme (i:ki=k) C(i)

I read that transitivity was the same as clustering coefficent.

I did

cluster=transitivit(G, type="local")

So I've got a vector containing value, and NA.

Q1: Does the value correspond to C(i) or C(k)?

Q2: Are the values ordered by degree (k) or by nodes in the vector?

Q3: If it's ordered by degree, I guess that the first degree in that is 1 since degree 0 has no neighbors?

If my values correspond to C(k) and are ordered by degree k, I though to do the following script to create my plot:

cluster=cluster[!is.na(cluster) #to remove NA

deg=degree(G) #to obtain list of degree

deg=unique(deg)#to remove duplicate

deg=sort(deg) # to order k degree

deg=deg[!deg==0] to remove k degree 0

length(deg)

length(cluster) # to check that both vectors have the same length

data="">

plot(data, type="o", xlab="k", ylab="c(k)")

Q4: Does it look ok?

Q5: for the mean of cluster coeffcient, If I remove the NA, its change the length of my vector so the mean, what is the correct mean in that case? 

Indeed, if I replace Na by zero, I've got a mean=0.222 (which match what I obtain in Gephi when I upload my file)

            if I suppress Na, I've got a mean=0.451. If it's 0.222 the right value, I just have to sum the vector obtained after removing NA and divide it by the number of nodes of my network.

Thanks in advance for any answers,

Delph