Multiscale Network Test (MNT)

Testing independence between network toplogy and nodal attributes via diffusion maps applied to distance-based correlations.

MNT Use

As an input of MNT, we require igraph object G, a vector or matrix representing nodal attributes X, types of test statistics, use of diffusion maps, a range of Markov time used for diffusion maps, and the number of permutation samples.

The following example tests independence between network topology of karate club and each member's faction.

library(igraphdata)
data(karate)
G = karate
X = V(karate)$Faction
res <- NetworkTest.diffusion.stat(G, X, option = 1, diffusion = TRUE,
                                  t.range = c(0:5), n.perm = 500)

The above prints out a list containing all the mgc statistics under the observations and under 500 permuations at Markov time t=0,1,2,..,5. The next command chooses the optimal diffusion map embeddings with dafault of t=3 and then we print out the p-value of network dependence test and optimal t.

res.optimal <- print.stat.optimal(res, default.t = 4)
print(res.optimal$pvalue)
print(res.optimal$alt.t)

Reference

Details of methods used for network dependence testing in the mgc package are described in arXiv.