Another popular algorithm for finding a minimum spanning tree is Kruskal's algorithm. It is similar to Prim's algorithm and uses a greedy approach to find the solution. Here are the steps we need to implement Kruskal's algorithm:

1. Create a forest T (a set of trees), where each vertex in the graph is a separate tree.
2. Create a set S containing all the edges in the graph.
3. While S is non-empty and T is not yet spanning:

1. Remove an edge with the minimum weight from S.

2. If that edge connects two different trees, then add it to the forest, combining two trees into a single tree; otherwise, discard that edge.

We will use the same graph that we used for Prim's algorithm. Here is the implementation of Kruskal's algorithm:

function Kruskal(array $graph): array { 
    $len = count($graph); 
    $tree = []; 

    $set = []; 
    foreach ($graph as $k => $adj) { 
    $set[$k] = [$k]; 
    } 

    $edges = []; 
    for ($i = 0; $i < $len; $i++) { 
      for ($j = 0; $j < $i; $j++) { 
        if ($graph[$i][$j]) { 
          $edges[$i . ',' . $j] = $graph[$i][$j]; 
        } 
    } 
    } 

    asort($edges); 

    foreach ($edges as $k => $w) { 
    list($i, $j) = explode(',', $k); 

    $iSet = findSet($set, $i); 
    $jSet = findSet($set, $j); 
    if ($iSet != $jSet) { 
        $tree[] = ["from" => $i, "to" => $j, 
    "cost" => $graph[$i][$j]]; 
        unionSet($set, $iSet, $jSet); 
    } 
    } 

    return $tree; 
} 

function findSet(array &$set, int $index) { 
    foreach ($set as $k => $v) { 
      if (in_array($index, $v)) { 
        return $k; 
      } 
    } 

    return false; 
} 

function unionSet(array &$set, int $i, int $j) { 
    $a = $set[$i]; 
    $b = $set[$j]; 
    unset($set[$i], $set[$j]); 
    $set[] = array_merge($a, $b); 
} 

As we can see, we have two separate functions—unionSet and findSet—to perform the union operations of two disjointed sets, as well as find out whether a number exists in a set or not. Now, let's run the program with our constructed graph like this:

$graph = [ 
    [0, 3, 1, 6, 0, 0], 
    [3, 0, 5, 0, 3, 0], 
    [1, 5, 0, 5, 6, 4], 
    [6, 0, 5, 0, 0, 2], 
    [0, 3, 6, 0, 0, 6], 
    [0, 0, 4, 2, 6, 0] 
]; 

$mst = Kruskal($graph); 

$minimumCost = 0; 

foreach($mst as $v) { 
    echo "From {$v['from']} to {$v['to']} cost is {$v['cost']} 
"; 
    $minimumCost += $v['cost']; 
} 

echo "Minimum cost: $minimumCost 
"; 

This will produce the following output, which is similar to our output from Prim's algorithm:

From 2 to 0 cost is 1
From 5 to 3 cost is 2
From 1 to 0 cost is 3
From 4 to 1 cost is 3
From 5 to 2 cost is 4
Minimum cost: 13

The complexity of Kruskal's algorithm is O (E log V), which is better than the generic implementation of Prim's algorithm.