  A projective network model is a model that enables predictions to be made
based on a subsample of the network data, with the predictions remaining
unchanged if a larger sample is taken into consideration. An exchangeable model
is a model that does not depend on the order in which nodes are sampled.
Despite a large variety of non-equilibrium (growing) and equilibrium (static)
sparse complex network models that are widely used in network science, how to
reconcile sparseness (constant average degree) with the desired statistical
properties of projectivity and exchangeability is currently an outstanding
scientific problem. Here we propose a network process with hidden variables
which is projective and can generate sparse power-law networks. Despite the
model not being exchangeable, it can be closely related to exchangeable
uncorrelated networks as indicated by its information theory characterization
and its network entropy. The use of the proposed network process as a null
model is here tested on real data, indicating that the model offers a promising
avenue for statistical network modelling.
