Title: Disentangling group and link persistence in Dynamic Stochastic Block models,
Abstract: We study the inference of a model of dynamic networks in which both
communities and links keep memory of previous network states. By considering
maximum likelihood inference from single snapshot observations of the network,
we show that link persistence makes the inference of communities harder,
decreasing the detectability threshold, while community persistence tends to
make it easier. We analytically show that communities inferred from single
network snapshot can share a maximum overlap with the underlying communities of
a specific previous instant in time. This leads to time-lagged inference: the
identification of past communities rather than present ones. Finally we compute
the time lag and propose a corrected algorithm, the Lagged Snapshot Dynamic
(LSD) algorithm, for community detection in dynamic networks. We analytically
and numerically characterize the detectability transitions of such algorithm as
a function of the memory parameters of the model and we make a comparison with
a full dynamic inference.