Compare relative to some null model, like the Configuration model, where –.–, and Y motifs are common, but cycles are rare, for instance.
See notes
Often a Polya-Aeppli distribution is suggested for motif counts, see Picard et al. 2008 . The Polya-Aeppli distribution is the distribution of W where W is the sum of a Poisson ( λ ) number of random variables, where each of the random variables follows a geometric(1 − a ) distribution, independently of each other (see the Monte Carlo example). In the random graph network, we can think of having a Poisson number of "clumps", and each clump having a geometric size.
When assessing the significance of two or more motifs, their dependence has to be taken into account, or else we resort to the Bonferroni correction, dividing the significance level of our tests by the number of tests carried out and using this as new significance level for each individual test.
Bonferroni correction: have 100 tests. I want a statistical significance (p-value) of 0.05. Then, each test should be performed with significance 0.05/100. Gets a lot of false negatives, but it really tries to prevent false positives. Metabolomics has a lot of tests, and so there are other alternatives..., but not an exact science..
Ego networks can be used to get replicas (samples) from same network. Need sparse networks for the egonets to be mostly independent.
Network motifs can be used to compare networks.