True scale-free networks hidden by finite size effects

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees by contrasting real data. Specifically, we analyze by finite-size scaling analysis the datasets of real networks to check whether purported departures from the power law behavior are due to the finiteness of the sample size. In this case, power laws would be recovered in the case of progressively larger cutoffs induced by the size of the sample. We find that a large number of the networks studied follow a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially infrastructure and transportation but also social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite-size effects due to the nature of the sample data

Prediction and modelling of complex social networks and their evolution.

This thesis focuses on complex social networks in the context of computational approaches for their prediction and modelling. The increasing popularity and advancement of social net- works paired with the availability of social network data enable empirical analysis, inference, prediction and modelling of social patterns. This data-driven approach towards social science is continuously evolving and is crucial for modelling and understanding of human social behaviour including predicting future social interactions for a wide range of applications. The main difference between traditional datasets and network datasets is the presence of the relational components (links) between instances (nodes) of the network. These links and nodes induce intricate local and global patterns, defining the topology of a network. The topology is ever evolving, determining the dynamics of such a networked system. The work presented in this thesis starts with an extensive analysis of three standard network models, in terms of their properties and self-interactions as well as the size and density of the resultant graphs. These crucial analysis and understanding of the main network models are utilised to later develop a comprehensive network simulation framework. A set of novel nature-inspired link prediction approaches are then developed to predict the evolution of networks, based solely on their topologies. Building on top of these approaches, enhanced topological representations of networks are subsequently combined with node characteristics for the purpose of node classification. Finally, the proposed classification methods are extensively evaluated using simulated networks from our network simulation framework as well as two real-world citation networks. The link prediction approaches proposed in this research show that the topology of the network can be further exploited to improve the prediction of future relationships. Moreover, this research demonstrates the potential of blending state-of-the-art Machine Learning techniques with graph theory. To accelerate such advancements in the field of network science, this research also offers an open- source software to provide high-quality synthetic datasets