A functional complexity framework for the analysis of telecommunication networks

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.