Create and plot a graph that represents a progression of university-level Mathematics courses. An edge between two courses signifies a course requirement.

A = [0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0]; names = {'Calculus I','Linear Algebra','Calculus II',...'Multivariate Calculus','Topology',...'Differential Equations','Real Analysis'}; G = digraph(A,names); plot(G)

Find the topological sorting of the courses to determine the proper order in which they should be completed.

N = toposort(G)

N =1 3 7 2 4 6 5

G。Nodes.Name(N,:)

ans =7x1 cell array{'Calculus I' } {'Calculus II' } {'Real Analysis' } {'Linear Algebra' } {'Multivariate Calculus' } {'Differential Equations'} {'Topology' }

Create a directed graph using a logical adjacency matrix, and then plot the graph.

rngdefault; A = tril(sprand(10, 10, 0.3), -1)~=0; G = digraph(A); [~,G] = toposort(G); plot(G)

Find the topological sorting of the graph nodes. Even thoughGis already in topological order,(1 2 3 4 5 6 7 8 9 10),toposortreorders the nodes.

toposort(G)

ans =2 1 4 10 9 8 5 7 3 6

SpecifyOrderas'stable'to use the stable ordering algorithm, so that the sort orders the nodes with smaller indices first. Stable sort does not rearrangeGif it is already in topological order.

toposort(G,'Order','stable')

ans =1 2 3 4 5 6 7 8 9 10