Network Management is an area of systems management. ITIL is about Service Management. Since the network is a keystone in the delivery of just about every modern day Service, all of the ITIL processes cover some aspects of Network Management. For example-

Service Operation:
Incident Mgt – Network related incidents
Problem Mgt – Network related errors in the infrastructure

Service Transition:
Config/Change/Release – Implementing changes to the network Configuration Items

Service Design:
Capacity/Availability – Pretty self explanatory
Service Level Management – The group that translates the business requirements into the technical requirements that the Network team act upon
ITSCM (Disaster Recover) – Um, yes please

IT has grown up thinking in terms of the systems it supports. This is natural and there need to be system specialists considering the “system” oriented issues. ITIL teaches us that we aren’t considering IT in its proper relation to supporting the Business unless there is someone thinking about Services, and how all the disparate systems join together to support those Services.

So, to answer your question – In which area should Network Management fall? All. And never in one specific area.