  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.
