The rapid evolution of network services demands new paradigms for studying and designing networks. In order to understand the underlying mechanisms that provide network functions, we propose a framework which enables the functional analysis of telecommunication networks. This framework allows us to isolate and analyse a network function as a complex system. We propose functional topologies to visualise the relationships between system entities and enable the systematic study of interactions between them. We also define a complexity metric $C_F$ (functional complexity) which quantifies the variety of structural patterns and roles of nodes in the topology. This complexity metric provides a wholly new approach to study the operation of telecommunication networks. We study the relationship between $C_F$ and different graph structures by analysing graph theory metrics in order to recognize complex organisations. $C_F$ is equal to zero for both a full mesh topology and a disconnected topology. We show that complexity is very high for a dense structure that shows high integration (shorter average path length and high average clustering coefficient). We make a connection between functional complexity, robustness and response to changes that may appear in the system configuration. We also make a connection between the implementation and the outcome of a network function which correlates the characteristics of the outcome with the complex relationships that underpin the functional structure.