refactor engine: decompose Holme-Kim into builder methods

The generator's working state (graph, attachment pool, rng) moves into
a holmeKimBuilder struct so each algorithm step is a small named
method: attachNewNode, link, pickMutualFriend, degreeProportionalSample.
Max nesting drops from five levels to two. The RNG call order is
untouched, and the golden test (99/70/7 reached) plus the fixed-seed
determinism test prove behaviour is bit-for-bit identical.
Go bits: pointer receivers ((b *holmeKimBuilder)) let methods mutate
the builder; (value, ok) multiple returns are the idiom for 'may not
exist', as in pickMutualFriend.

internal/engine/holmekim.go

@@ -26,77 +26,102 @@ func HolmeKim(numNodes, edgesPerNode int, triangleProb float64, rng *rand.Rand)
 		return nil, fmt.Errorf("holme-kim: need 0 <= triangleProb <= 1, got %v", triangleProb)
 	}
 
-	graph := NewGraph(numNodes)
+	builder := holmeKimBuilder{graph: NewGraph(numNodes), rng: rng}
-
+	// Seed the pool with the first edgesPerNode nodes so the earliest
-	// One entry per edge endpoint, so sampling uniformly from this list is
+	// arrivals have someone to connect to.
-	// sampling nodes proportionally to their degree: that is the whole
+	for node := range edgesPerNode {
-	// "preferential attachment" trick. Seeded with the first edgesPerNode
+		builder.pool = append(builder.pool, node)
-	// nodes so the earliest arrivals have someone to connect to.
-	attachmentPool := make([]int, edgesPerNode)
-	for node := range attachmentPool {
-		attachmentPool[node] = node
 	}
-
 	for newNode := edgesPerNode; newNode < numNodes; newNode++ {
-		// Where this node could attach: edgesPerNode distinct existing
+		builder.attachNewNode(newNode, edgesPerNode, triangleProb)
-		// nodes, drawn degree-proportionally. Consumed from the end.
-		candidates := degreeProportionalSample(attachmentPool, edgesPerNode, rng)
-
-		target := candidates[len(candidates)-1]
-		candidates = candidates[:len(candidates)-1]
-		graph.AddEdge(newNode, target)
-		attachmentPool = append(attachmentPool, target)
-
-		for edgesAdded := 1; edgesAdded < edgesPerNode; {
-			// Triangle step: with probability triangleProb, also link to a
-			// friend of the node we just attached to.
-			if rng.Float64() < triangleProb {
-				var mutualCandidates []int
-				for _, friendOfTarget := range graph.Neighbors(target) {
-					if friendOfTarget != newNode && !graph.HasEdge(newNode, friendOfTarget) {
-						mutualCandidates = append(mutualCandidates, friendOfTarget)
 	}
-				}
+	return builder.graph, nil
-				if len(mutualCandidates) > 0 {
+}
-					mutualFriend := mutualCandidates[rng.IntN(len(mutualCandidates))]
+
-					graph.AddEdge(newNode, mutualFriend)
+// holmeKimBuilder carries the generator's working state so each step of the
-					attachmentPool = append(attachmentPool, mutualFriend)
+// algorithm reads as a small named method instead of one deeply nested loop.
-					edgesAdded++
+type holmeKimBuilder struct {
+	graph *Graph
+	// pool holds one entry per edge endpoint, so sampling uniformly from it
+	// picks nodes proportionally to their degree: that is the whole
+	// "preferential attachment" trick.
+	pool []int
+	rng  *rand.Rand
+}
+
+// attachNewNode links newNode to edgesPerNode existing nodes: preferential
+// attachment by default, a friend-of-a-friend triangle with probability
+// triangleProb.
+func (b *holmeKimBuilder) attachNewNode(newNode, edgesPerNode int, triangleProb float64) {
+	// Where this node could attach: edgesPerNode distinct existing nodes,
+	// drawn degree-proportionally, consumed from the end.
+	candidates := b.degreeProportionalSample(edgesPerNode)
+
+	target := popLast(&candidates)
+	b.link(newNode, target)
+
+	for edgesAdded := 1; edgesAdded < edgesPerNode; edgesAdded++ {
+		if b.rng.Float64() < triangleProb {
+			if mutualFriend, found := b.pickMutualFriend(newNode, target); found {
+				b.link(newNode, mutualFriend)
 				continue
 			}
 		}
-			// Otherwise (or if no triangle was possible): plain
+		// Plain preferential attachment. Mirrors networkx, including the
-			// preferential attachment to the next candidate. Mirrors
+		// quirk that a candidate already linked via a triangle step counts
-			// networkx, including the quirk that a candidate already linked
+		// as an attempt without adding an edge, so a node can end up with
-			// via a triangle step counts as an attempt without adding an
+		// slightly fewer than edgesPerNode edges.
-			// edge, so a node can end up with slightly fewer than
+		target = popLast(&candidates)
-			// edgesPerNode edges.
+		b.link(newNode, target)
-			target = candidates[len(candidates)-1]
-			candidates = candidates[:len(candidates)-1]
-			graph.AddEdge(newNode, target)
-			attachmentPool = append(attachmentPool, target)
-			edgesAdded++
 	}
 
 	// The new node enters the pool once per edge slot, like networkx.
 	for range edgesPerNode {
-			attachmentPool = append(attachmentPool, newNode)
+		b.pool = append(b.pool, newNode)
 	}
-	}
-	return graph, nil
 }
 
-// degreeProportionalSample draws sampleSize distinct nodes from the pool.
+// link adds the edge and records the endpoint in the attachment pool,
-// The pool holds one entry per edge endpoint, so nodes with more edges are
+// raising target's future attachment odds.
-// proportionally more likely to be drawn. networkx returns a Python set
+func (b *holmeKimBuilder) link(newNode, target int) {
-// here; we keep a slice in draw order so the result is deterministic.
+	b.graph.AddEdge(newNode, target)
-func degreeProportionalSample(pool []int, sampleSize int, rng *rand.Rand) []int {
+	b.pool = append(b.pool, target)
+}
+
+// pickMutualFriend draws a random neighbour of target that newNode is not
+// already connected to; closing that link forms a triangle. found is false
+// when no such neighbour exists.
+func (b *holmeKimBuilder) pickMutualFriend(newNode, target int) (mutualFriend int, found bool) {
+	var candidates []int
+	for _, friendOfTarget := range b.graph.Neighbors(target) {
+		if friendOfTarget != newNode && !b.graph.HasEdge(newNode, friendOfTarget) {
+			candidates = append(candidates, friendOfTarget)
+		}
+	}
+	if len(candidates) == 0 {
+		return 0, false
+	}
+	return candidates[b.rng.IntN(len(candidates))], true
+}
+
+// degreeProportionalSample draws sampleSize distinct nodes from the pool;
+// nodes with more edges appear more often there, so they are
+// proportionally more likely. networkx returns a Python set here; we keep
+// a slice in draw order so the result is deterministic.
+func (b *holmeKimBuilder) degreeProportionalSample(sampleSize int) []int {
 	sample := make([]int, 0, sampleSize)
 	for len(sample) < sampleSize {
-		drawn := pool[rng.IntN(len(pool))]
+		drawn := b.pool[b.rng.IntN(len(b.pool))]
 		if !slices.Contains(sample, drawn) {
 			sample = append(sample, drawn)
 		}
 	}
 	return sample
 }
+
+// popLast removes and returns the last element of the slice.
+func popLast(stack *[]int) int {
+	last := (*stack)[len(*stack)-1]
+	*stack = (*stack)[:len(*stack)-1]
+	return last
+}