CyNetworkTableManager lets you associate tables with networks. The "type" parameter in setTable() determines whether the table will be a network-, node-, or edge-specific table. This means the primary key of the table will be network, node, or edge SUIDs, respectively. Right now, it's not possible to associate an arbitrary table with a network (i.e. tables where the primary key doesn't correspond to SUIDs of networks, nodes, or edges).
A network's tables are organized by namespace. The tables displayed by the table browser have the namespace CyNetwork.DEFAULT_ATTRS. Networks also have tables in the namespace CyNetwork.HIDDEN_ATTRS. These are internal identifiers that the user will likely never see. A network can only have one table for each (type, namespace) pair; e.g. a network can only have one CyNode table in the CyNetwork.DEFAULT_ATTRS namespace.