Abstract
This chapter is an introduction to complex networks theory, emphasising its application to air route networks. Complex networks theory is one of the most fruitful outcomes of systems theory, an interdisciplinary approach to natural and social reality considering relationships between elements. Here we introduce measures of structural properties of complex networks. These measures allow us to evaluate the existence of the small-world property and the presence of heterogeneous degree distributions. Next, we present a brief introduction of assortative mixing, modularity and community detection in networks. We finish the chapter by presenting the most common theoretical models of complex networks: the Erdös–Rényi model of random networks, the Watts–Strogatz model of small world networks and the Barabási–Albert model of scale-free networks.
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