Basic Graph Theory with Applications to Economics

Let N = {1, . . . , n} be a finite set. Let E be a collection of ordered or unordered pairs of distinct 1 elements from N . A graph G is defined by (N,E). The elements of N are called vertices of graph G. The elements of E are called edges of graph G. If E consists of ordered pairs of vertices, then the graph is called a directed graph (digraph). When we say graph, we refer to undirected graph, i.e., E consists of unordered pairs of vertices. To avoid confusion, we write an edge in an undirected graph as {i, j} and an edge in a directed graph as (i, j). Figure 1 gives three examples of graphs. The rightmost graph in the figure is a directed graph. In all the graphs N = {1, 2, 3, 4}. In the leftmost graph in Figure 1, E = {{1, 2}, {2, 3}, {2, 4}, {3, 4}}. In the directed graph, E = {(1, 2), (1, 3), (2, 3), (3, 2), (3, 4), (4, 1)}.