Create and plot a directed graph.

G = digraph([1 2 3 4 4 4 5 5 5 6 7 8],[2 3 5 1 3 6 6 7 8 9 9 9]); plot(G)

Find the transitive closure of graphGand plot the resulting graph.Hcontains the same nodes asG, but has additional edges.

H = transclosure(G); plot(H)

The transitive closure information inHcan be used to answer reachability questions about the original graph,G.

Determine the nodes inGthat can be reached from node 1. These nodes are the successors of node 1 in the transitive closure graph,H.

N = successors(H,1)

N =7×12 3 5 6 7 8 9

Create and plot a directed graph.

s = [1 1 2 2 3 4 4 5]; t = [2 4 3 4 5 5 6 6]; G = digraph(s,t); plot(G,'Layout','subspace')

Calculate the adjacency matrix of the transitive closure ofG. The result is areachabilitymatrix, which has nonzero values to indicate which nodes are reachable from each node.

D = transclosure(G); R = full(adjacency(D))

R =6×60 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0

For example, to answer the question "Which nodes are reachable from node 3?", you can look at the third row in the matrix. That row indicates only nodes 5 and 6 are reachable from node 3:

find(R(3,:))

ans =1×25 6