Chapter 28: Graph Theory and Networks
Cassey Lee The economy is obviously a complex entity characterized by interactions between multiple and heterogenous agents over time. Many attempts have been made to visually represent and model such interactions. One approach that has been increasingly used involves the use of tools and concepts from a branch of mathematics known as graph theory. Its origin dates back to Euler’s solution of the ‘Königsberg Bridge Problem’ in 1736. In the social sciences, sociologists have been early enthusiasts of graph theory. The history of ‘social network analysis’ (SNA) dates back to the 1930s, with significant breakthroughs in the 1960s (Scott, 1991). In economics, some of the early studies employing graph theory can be traced back to the second half of the 1990s. It took roughly another 15 years before it became the basis of a new field of study in economics under the banner of ‘social networks’. The term ‘graph theory’ should not be confused with the economists’ common use of the word ‘graph’, which usually refers to a twodimensional Cartesian representation of equations. Graph theory is a study of the properties of graphs, where a graph is a set of vertices (dots) connected by edges (lines). Figure 28.1 provides a depiction of a graph with five vertices. For a graph with n vertices, the maximum number of edges m is given by the formula: m5 n (n 2 1) 2 In the example shown in Figure 28.1, the five vertices are connected by ten edges. Beyond such basics, various...
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