Creating and Describing Networks

Kimmo Soramäki and Samantha Cook

There are many different network structures that arise naturally or have proven to be useful for modelling real phenomena. This chapter will present many different types of networks and show how to generate instances of them. In addition, it will depict some common network summary measures that are useful for describing and comparing networks.

THE LANGUAGE OF NETWORKS

A graph is a set of nodes (also commonly referred to as vertices), pairs of which may be joined by links (also commonly referred to as edges in undirected networks, or arcs in directed networks; see below for the definitions of directed/undirected networks). For example, in a graph whose nodes represent people, the links could represent friendships or family relationships. Geographic locations can be linked by motorway or airline route. We have already introduced payment systems and asset correlation networks as examples of financial networks. Nodes and links may have properties, and we use the term “network” to refer to graphs with properties. In a network where nodes represent banks and links represent payments, for example, node properties might include total holdings, location of the company headquarters and