Simplifying large-scale communication networks with weights and cycles

Abstract

A communication network is a complex network designed to transfer information from a source to a destination. One of the most important property in a communication network is the existence of alternative routes between a source and destination node. The robustness and resilience of a network are related to its path diversity (alternative routes). Describing all the components and interactions of a large communication network is not feasible. In this thesis we develop a new method, the deforestation algorithm, to simplify very large networks, and we called the simplified network the skeleton network. The method is general. It conserves the number of alternative paths between all the sources and destinations when doing the simplification and also it takes into consideration the properties of the nodes, and the links (capacity and direction). When simplifying very large networks, the skeleton networks can also be large, so it is desirable to split the skeleton network into different communities. In the thesis we introduce a community-detection method which works fast and efficient for the skeleton networks. Other property that can be easily extracted from the skeleton network is the cycle basis, which can suffice in describing the cycle structure of complex network. We have tested our algorithms on the Autonomous System (AS)l evel and Internet Protocol address (IPA)le vel of the Internet. And we also show that deforestation algorithm can be extended to take into consideration of traffic directions and traffic demand matrix when simplifying medium-scale networks. Commonly, the structure of large complex networks is characterised using statistical measures. These measures can give a good description of the network connectivity but they do not provide a practical way to explore the interaction between the dynamical process and network connectivity. The methods presented in this thesis are a first step to address this practical problem.