  The stochastic block model (SBM) is a widely used framework for community
detection in networks, where the network structure is typically represented by
an adjacency matrix. However, conventional SBMs are not directly applicable to
an adjacency matrix that consists of non-negative zero-inflated continuous edge
weights. To model the international trading network, where edge weights
represent trading values between countries, we propose an innovative SBM based
on a restricted Tweedie distribution. Additionally, we incorporate nodal
information, such as the geographical distance between countries, and account
for its dynamic effect on edge weights. Notably, we show that given a
sufficiently large number of nodes, estimating this covariate effect becomes
independent of community labels of each node when computing the maximum
likelihood estimator of parameters in our model. This result enables the
development of an efficient two-step algorithm that separates the estimation of
covariate effects from other parameters. We demonstrate the effectiveness of
our proposed method through extensive simulation studies and an application to
real-world international trading data.
