The network data model structures data as record types, with pointer links to allow to navigate between one record and another. So to query a network data model you begin at one record and move around pointer references.
Network model data bases fell out of favor a while ago to the RelationalDataModel, but this data model is by no means dead. Indeed it's the primary model for in-memory data. Almost every mainstream language has facilities for defining record types and pointers.
You can think of object models as a form of network data model, since they also have data structures linked by pointers. The vital difference is that objects incorporate data and behavior, as a result I think they feel much different in practice. However many object models (AnemicDomainModel) are really only network data models since they don't have any significant behavior.