/**
* Traverse the graph using DFS to detect cycles
* @param Graph $g
* @param mixed $x0
* @return boolean Whether the graph contains cycles
*/
public static function containsCycle(Graph $g, $x0 = null)
{
//We are assuming that the graph is directed
if (!$g->directed) {
//If it is not, it is cyclic if it has edges
return $g->size > 0;
}
$cyclic = false;
$func = function (Vertex $v, array $discovered, array $recursionStack) use(&$cyclic) {
$adjacentVertices = $v->getAdjacentVertices();
//Loop edge
if (in_array($v, $adjacentVertices)) {
$cyclic = true;
}
//This is needed for directed graphs
if (array_intersect($adjacentVertices, $recursionStack) !== []) {
$cyclic = true;
}
//Stop traversing if the graph is cyclic
return !$cyclic;
};
if ($x0 === null) {
$vertices = $g->getSourceVertices();
if (empty($vertices)) {
//If the graph has no source vertices
//the graph is cyclic
return true;
}
//The graph should be checked from every source vertex
//There may be cyclic subgraphs that could be missed otherwise
$visited = [];
foreach ($vertices as $vertex) {
$visited = array_merge($visited, static::dfs($g, $vertex->label, $func));
}
//Check if there are any subgraphs without sources (not visited by above algorithm)
if (count(array_unique($visited)) !== $g->order) {
return true;
}
} else {
//A specific vertex is given - check the reachable subgraph only
static::dfs($g, $x0, $func);
}
return $cyclic;
}
