3 research outputs found
Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models
W-graph refers to a general class of random graph models that can be seen as
a random graph limit. It is characterized by both its graphon function and its
motif frequencies. In this paper, relying on an existing variational Bayes
algorithm for the stochastic block models along with the corresponding weights
for model averaging, we derive an estimate of the graphon function as an
average of stochastic block models with increasing number of blocks. In the
same framework, we derive the variational posterior frequency of any motif. A
simulation study and an illustration on a social network complete our work
Motif-based tests for bipartite networks
Bipartite networks are a natural representation of the interactions between
entities from two different types. The organization (or topology) of such
networks gives insight to understand the systems they describe as a whole.
Here, we rely on motifs which provide a meso-scale description of the topology.
Moreover, we consider the bipartite expected degree distribution (B-EDD) model
which accounts for both the density of the network and possible imbalances
between the degrees of the nodes. Under the B-EDD model, we prove the
asymptotic normality of the count of any given motif, considering sparsity
conditions. We also provide close-form expressions for the mean and the
variance of this count. This allows to avoid computationally prohibitive
resampling procedures. Based on these results, we define a goodness-of-fit test
for the B-EDD model and propose a family of tests for network comparisons. We
assess the asymptotic normality of the test statistics and the power of the
proposed tests on synthetic experiments and illustrate their use on ecological
data sets
Compound Poisson approximations of subgraph counts in random graphs
SIGLEAvailable from British Library Document Supply Centre-DSC:4335.26206(98-22) / BLDSC - British Library Document Supply CentreGBUnited Kingdo