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Re: [igraph] motifs

From: Manuel Zetina-Rejon
Subject: Re: [igraph] motifs
Date: Fri, 14 Oct 2016 02:58:58 -0600

Hi Tamas!

Thank you very much for your reply. Actually, it makes sense to me on the use of connected subgraphs as motifs, in the sense that an isolated vertex doesn’t play a important role in the subgraph structure.

On the other hand, motifs() returns a vector with the number of occurences of each motif in the graph ordered by their isomorphism class. How do I know which isomorphism class are present in my graph. I mean, a possible result of motifs(graph, size =3) could be something like this:
> NA NA 32 18

For me, this means that there are 32 motifs of x-isomorphic class and other 18 motifs of y-isomorphic class. But, which classes? I’ve playing with something like this to explore how all possible isomorphic classes (n = 3) look like:

iso <- vector(mode = "list", length = 3)
iso.class <- 1:length(iso)

for(i in 1:length(iso)){
  iso[[i]] <- graph_from_isomorphism_class(3, i, directed = FALSE)
iso[[i]]$name <- paste("Class", iso.class[i])

par(mfrow = c(1,3))
for(i in 1:length(iso)){
plot(iso[[i]], layout = layout_in_circle(iso[[i]]),  main = iso[[i]]$name)

But How do I know which of them are present in the original graph?

Thank you very much!


El 14/10/2016, a las 02:31, Tamas Nepusz <address@hidden> escribió:


I haven't read the papers once again, but in my opinion a disconnected
motif doesn't really make sense. Consider a disconnected motif that
consists of a fully connected triangle and an additional isolated
vertex, and then take a graph that contains one triangle and one
million isolated vertices. Does that really mean that this "motif"
appears one million times in the graph? Is that a significant finding?
If I added an additional one million totally unrelated vertices to the
graph, does that make the motif appear twice as frequently?

Anyway, if you want to search for disconnected patterns in a graph,
you can still use count_subgaph_isomorphisms() with method="lad" and
induced=TRUE; see:


It will be much slower, though -- searching for connected motifs is
much easier if the average degree of a vertex is low.


On Fri, Oct 14, 2016 at 8:59 AM, Manuel Zetina-Rejon <address@hidden> wrote:
Hi Guys!

This is probably a basic question, but I don’t find the clear criteria or reference, why in igraph help, you mention that unconnected subgraphs (of x isomorphic class) are not considered motifs? For that reason, motifs() is NA for unconnected subgraphs. It is also not clear if you mean strongly or weakly connected subgraphs

According to Milo et al. (2002) and Shen-Orr et al. (2002) motifs are not necessarily connected, even in directed graphs.

Thank you for your opinions

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