hascycles

Determine whether graph contains cycles

Since R2021a

Syntax

tf = hascycles(G)

Description

tf = hascycles(G) returns logical 1 (true) if graph G contains one or more cycles, and logical 0 (false) otherwise.

Examples

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Determine Whether Undirected Graph Has Cycles

Open Live Script

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

Determine Whether Directed Graph Has Cycles

Open Live Script

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.

Input Arguments

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`G` — Input graph
`graph` object | `digraph` object

Input graph, specified as either a graph or digraph object. Use graph to create an undirected graph or digraph to create a directed graph.

Example: G = graph(1,2)

Example: G = digraph([1 2],[2 3])

More About

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Graph Cycles

A cycle exists in a graph when there is a nonempty path in which only the first and last nodes are repeated. An example of a cycle is: (Node1 - Node2 - Node3 - Node1).

A cycle cannot traverse the same edge twice. For example, the cycle (Node1 - Node2 - Node1) in an undirected graph only exists if there is more than one edge connecting Node1 and Node2. By this definition, self-loops count as cycles, though they cannot be part of any larger cycles.