finally, the link strength or weight, which characterizes the nature of the interactions between different nodes.

Based on these measures, real networks may be classified in perhaps two or three major classes. First, there is a class known as regular networks, or graphs, in which the degree of all the nodes assumes the same value or only a few discrete values and the underlying network has a regular, repetitive structure. Such regular graphs approximate the structure of most crystals, as well as a number of other objects, engineered and natural, from the retina of the eye to the roads of some large cities (like New York). Much attention, however, has focused on random networks, systems in which the nodes are randomly connected to each other. In such networks the degrees follows a Poisson distribution. Despite their important role in network theory, we do not know of major real networks that would be fully random. Finally, the availability of large-scale network maps has led to the discovery that many real networks are neither regular nor fully random but, rather, scale-free. They have a heavily tailed degree distribution—that is, there are significant (order of magnitude) differences in the degree of different nodes. Scale-free networks describe the cell, the Web, the Internet, and many collaboration and social and economic networks. While many real networks are intermediate between these three classes, this classification captures some of the basic primitives used in many courses on networks and most networks are characterized in terms of the three classes.

An important question surfacing in many network-science-related courses is the following: What processes and mechanisms give rise to the network characteristics discussed in the preceding section? A closely related question is this: How do we generate networks with structural characteristics that mimic the properties of selected real networks? Network models, introduced to answer these two questions, are an important part of most network science courses (see Table C-4). These models have two main functions. First, some models aim to mimic, in a simplified form, the emergence and evolution of real networks, helping us to understand the mechanism responsible for the formation of real networks. Second, to test the impact of selected network characteristics on the network’s behavior, we need to gener-