Evolving Properties of Growing Networks

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...

Universality for distances in power-law random graphs

We survey the recent work on phase transition and distances in various random graph models with general degree sequences. We focus on inhomogeneous random graphs, the configuration model, and affine preferential attachment models, and pay special attention to the setting where these random graphs have a power-law degree sequence. This means that...

ELASTICITY: Topological Characterization of Robustness in Complex Networks

Characterization of complex networks: Application to robustness analysis

This thesis focuses on the topological characterization of complex networks. It specifically focuses on those elementary graph measures that are of interest when quantifying topology-related aspects of the robustness of complex networks. This thesis makes the following contributions to the field of complex networks. Firstly, the thesis analyses...

Random graphs: From static to dynamic

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...