  Nonextensivity is foreseeable in network ensembles, as heterogeneous
interactions generally exist in complex networked systems that need to be
described by network ensembles. But this nonextensivity has not been
literatured proved yet. In this work, the existence of nonextensivity in the
binary and weighted network ensembles is theoretically proved for the first
time (both in the microcanonical and canonical ensemble) based on the finding
of the local entropy's nonlinear change when new nodes are added to the network
ensembles. This proof also shows that the existence of nonextensivity is the
main difference between the network ensembles and other traditional models in
statistical physics (Ising model).
