A motif in a network is a connected subgraph that occurs significantly more frequently as an induced subgraph than would be expected in a similar random network.
From what I've read in various papers, it seems that the vast majority of interest in network motifs is focussed on k-node motifs for k=3,4,5 (and infrequently k=6). The only papers I've seen talking about motifs of size k=7,8,... are papers that introduce motif detection algorithms, touting the additional functionality of these programs.
Now I'm working on a program with a group in China which can achieve respectable speedups vs. Kavosh for k<=6 (but no functionality for k>=7). I'm planning on making the following claim in our paper:
...the majority of real-world attention has, so far, been on k-node motifs where k is quite small (3<=k<=6).
In fact, this is why we have focused our attention on the k<=6 cases. From what I've encountered so far, this is accurate. However, I would like to gauge the communities response to this claim, just in case I have somehow encountered a misleading sample of papers.
Question: Is the above claim accurate?
PS. I recognise that there are certain k-node subgraphs in networks that are considered important, but are not motifs (in that they do not appear with abnormal frequency).
EDIT: Well, perhaps it's difficult to answer the above question in the affirmative (if it were true, and it seems to be). So here is are two, more focussed questions.
Question: Is anyone currently working with k-node network motifs (where k>=7)?
Question: Are there any research papers that involve k-node network motifs (where k>=7)?
I'm aiming for applications with the above questions, rather than implementation.