Evolving Properties of Growing Networks

Abstract

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.