hascycles

Create and plot an undirected graph.

G = graph([1 1 1 1],[2 3 4 5]);
plot(G)

Determine whether the graph has cycles.

tf = hascycles(G)

tf = logical
   0

Now add an edge to the graph between node 2 and node 3. Replot the graph.

G = addedge(G,2,3);
plot(G)

Determine whether the new graph has cycles.

tf2 = hascycles(G)

tf2 = logical
   1

Examine the difference between the hascycles and isdag functions operating on a directed graph.

Create and plot a directed graph.

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

Determine whether the graph contains any cycles.

tf = hascycles(G)

tf = logical
   1

hascycles returns true when a directed graph contains a cycle.

Now, use isdag to determine whether the graph is directed and acyclic.

tf2 = isdag(G)

tf2 = logical
   0

isdag returns false because the graph contains a cycle. In general, the hascycles and isdag functions return opposite results for directed graphs.