Cluster damage robustness analysis and space independent community detection in complex networks

Abstract

This thesis investigates the evolution of two very different complex systems using network theory. This multi-disciplinary technique is widely used to model and analyse vastly diverse systems of multiple interacting components, and therefore, it is applied in this thesis to study the complexity of the systems. This complexity is rooted in the components’ interactions such that the whole system is more than the sum of all the individual parts. The first novelty in this research is the proposal of a new type of structural perturbation, cluster damage, for measuring another dimension of network robustness. The second novelty is the first application of a community detection method, which uncovers space-independent communities in spatial networks, to airport and linguistic networks. A critical property of complex systems – robustness – is explored within a partial model of the Internet, by demonstrating a novel perturbation strategy based on the iterative removal of clusters. The main contribution of this theoretical case study is the methodology for cluster damage, which has not been investigated by literature on the robustness of complex networks. The model, part of the Internet at the Autonomous System level, only serves as a domain where the novel methodology is demonstrated, and it is chosen because the Internet is known to be robust due to its distributed (non-centralised) nature, even though it is often subjected to large perturbations and failures. The first applied case study is in the field of air transportation. Specifically, it explores the topology and passenger flows of the United States Airport Network (USAN) over two decades. The network model consists of a time-series of six network snapshots for the years 1990, 2000 and 2010, which capture bi-monthly passenger flows among US airports. Since the network is embedded in space, the volume of these flows is naturally affected by spatial proximity, and therefore, a model (recently proposed in the literature) accounting for this phenomenon is used to identify the communities of airports that have particularly high flows among them, given their spatial separation. The second applied case study – in the field of language acquisition – investigates the word co-occurrence network of children, as they develop their linguistic abilities at an early age. Similarly to the previous case study, the network model consists of six children and three discrete developmental stages. These networks are not embedded in physical space, but they are mapped to an artificial semantic space that defines the semantic distance between pairs of words. This novel approach allows for an additional dimension of network information that results in a more complete dataset. Then, community detection identifies groups of words that have particularly high co-occurrence frequency, given their semantic distance. This research highlights the fact that some general techniques from network theory, such as network modelling and analysis, can be successfully applied for the study of diverse systems, while others, such as community detection, need to be tailored for the specific system. However, methods originally developed for one domain may be applied somewhere completely new, as illustrated by the application of spatial community detection to a non-spatial network. This underlines the importance of inter-disciplinary research.