This chapter discusses random and naturally occurring networks. We look at their properties as well as some algorithms for computing those properties.

Networks and Graphs

In the literature, the terms network and graph often are used interchangeably. Here, we use network to indicate a representation of a natural relationship among objects (in the context of this book, mostly linguistic objects) and graph for relationships generated through an automatic process. Furthermore, networks have a more complex structure than some types of graphs, such as lattices (i.e., predictable degree) or random graphs (i.e., completely arbitrary edges).

Network theory is a relatively new field. Apart from classic papers that appeared in the literature for other domains of science (e.g., economics and information science), most work in this field has been published since 1998.

The field of network theory studies the behavior of networks (mostly naturally occurring networks), for example, among people, drugs, animals, and scientific papers – under specific assumptions. It is concerned with the measurement of certain topological aspects of networks such as their degree distribution (i.e., how many nodes are connected to a specific node), the distribution of their connected components, and their diameter (e.g., the maximal distance between any two arbitrarily chosen nodes). Some properties can be computed exactly, in closed form, whereas others are computed using sampling. One goal of network theory is to predict the extrinsic behavior of a network based on its measurable properties.