· · · Institutional Repository

Complex networks describe a wide range of systems and structures in the world. Any real network can be modeled as graph, expressed by an adjacency matrix or list. In many complex networks, when a graph of a certain type grows in size, its properties are expected to change. Each complex network presents specific topological features which characterize its individual properties and are influenced by the dynamics of processes executed on the network. The analysis of complex networks therefore relies on the use of measurements capable of expressing the most relevant topological features. Therefore, understanding and analyzing the properties of different sized graphs is a challenging topic in the research field. The objective of the thesis is to understand the evolving properties of growing networks. Therefore it focuses on comparison of topological metrics with different number of nodes and links. Growing graphs will be approached by two different schemes: preferential link attachment and random link attachment. Several common types of graph models are involved in the thesis. And we also consider different real-world network examples. With the analysis and comparison of numerical simulation results, we want to understand the changing tendency of topological metrics for evolving networks. In final, the thesis reveals different crucial factors affecting the evolving properties of growing network and concludes evolving properties based on both empirical and analytical results.

Holons are universal and omni-present. They are organized in holarchies (hierarchical networks). Networks change continuously over time. At the aggregation level of the Sector Network and of the Telecom Network, diverse drivers cause changes. To provide for a better quality of life, trans-sector orchestration of change is required. Therefore, it is imperative to understand the sector network architecture, the major dilemmas, the drivers causing change and the interdependency with outer aggregation levels. In the Sector Network, households historically had a predominantly consumptive role. But they are increasingly becoming producers, or prosumers. Therefore, the introduction of the Smart Living concept into households will fuel the Sector Network evolution pro-foundly. Consequently, the infuence of the Smart Home on the Sector Network and its lower aggregates, like the Telecom Network, also will be signifcant. This thesis mainly investigates the drivers that infuence telecom transport network changes over time as well as the sector network dynamics over time, thereby providing insight into trans-sector orchestration over network evolution.

Power transmission networks are large scale complex distributed and networked systems, situated in dynamic environments. Managing such systems is essentially decentralized and distributed. The main function of power transmission grids is to assure the security and reliability of the network and to avoid blackouts. Key elements that can determine the security and reliability in transmitting power are the grids topological structures as well as their physical and operational behaviors and states. The capacity of a network to cope with disturbance imposed on it defines its degree of robustness. In assessing power grids reliability, their robustness and vulnerability against failures (both random failures and intentional attacks) must be taken into account. The secure delivery of power as well as the ability to protect and react to power outage and failures must be done in a distributed environment. Improving the robustness of the grids in distributed environment with no centralized control and management is a challenge. This work propose an effective theoretical method based on complex network approaches for improving robustness of power transmission networks dynamically by reducing their vulnerability in a decentralized and distributed environment. The method is applied to test a grid system to demonstrate its effectiveness on improving the networks robustness.

Many empirical studies on real-life networks show that many networks are small worlds, meaning that typical distances in these networks are small, and many of them have power-law degree sequences, meaning that the number of nodes with degree k falls off as kˆ (-τ) for some exponent τ>1. These networks are modeled by means of scale-free random graphs. One way to construct such a random graph is to start with a fixed number of nodes and randomly add edges between pairs of nodes. Using a growth model is a second way to construct a random graph. In such a model one starts with a given graph, and at each discrete time step a new node is added to the graph and the node is connected to some of the old nodes, where nodes with a high number of edges are preferred (preferential attachment). In this thesis two types of random graphs are considered: static random graphs and dynamic random graphs. A static random graph aims to describe a network and its topology at a given time instant, and a dynamical random graph aims to explain how the network came to be as it is. In this thesis two static random graphs are studied which produce power-law degree sequences: 'the configuration model' and 'the inhomogeneous random graph'. Two dynamic random graphs are introduced: 'the preferential attachment model with random initial degrees' and 'the geometric preferential attachment model with fitness'. In this thesis the degree sequence, the typical distance and the diameter for each of the models is considered, which are influenced by the power-law exponent τ. If τ>3, then each node in the graph has the same kind of neighborhood and the typical distance is proportional to log(n) if the graph consists of n nodes. If τ∈(2,3), then nodes with a high degree will appear and the typical distance is proportional to loglog(n). If τ∈(1,2), then the graph has a star-shaped structure and the distance is bounded by some constant.