They are used to model real-world systems such as the Internet (each node represents a router and each edge represents a connection between routers); airline connections (each node is an airport and e...They are used to model real-world systems such as the Internet (each node represents a router and each edge represents a connection between routers); airline connections (each node is an airport and each edge is a flight); or a city road network (each node represents an intersection and each edge represents a block).
Mathematically, a (directed) graph is a pair \(G=(V,E)\) where \(V\) is a set of vertices and \(E\) is a set of ordered pairs of vertices called edges. For example, in a university setting we might ha...Mathematically, a (directed) graph is a pair \(G=(V,E)\) where \(V\) is a set of vertices and \(E\) is a set of ordered pairs of vertices called edges. For example, in a university setting we might have a timetable conflict graph whose vertices represent courses offered in the university and in which the edge \(\mathtt{(i,j)}\) is present if and only if there is at least one student that is taking both class \(\mathtt{i}\) and class \(\mathtt{j}\).
