One network monitoring system maintains information regarding historical activity and emergent activity of the network. Comparison of recent with historical activity allows the system to determine whether recent activity is within the realm of normal. The system maintains data structures representing a p.d.f. for observable values of network parameters. Another network monitoring device includes data structures for maintaining information regarding historical and emergent activity of a network. This network monitoring device maintains those data structures including information regarding historical and emergent activity of a network only for those source/destination pairs, and only for those nodes, for which maintaining that information would be substantially meaningful. Yet another network monitoring system includes data structures for maintaining information regarding historical and emergent activity of a network that maintains those data structures only for those combinations of more than one of those multiple profile dimensions for which maintaining that information would be substantially meaningful.