fix: correct mcs algorithm to check earlier neighbors in chordal detection

the maximum cardinality search algorithm for chordal graph detection
was incorrectly checking if "later" neighbors form a clique, when it
should check "earlier" neighbors (vertices appearing before the current
vertex in the elimination ordering).

this fix ensures trees and other chordal graphs are correctly
identified by the isChordalUndirectedBinary predicate.

Author: Mearman

src/analyzer/predicates.ts

@@ -189,25 +189,25 @@ const isChordalUndirectedBinary = (g: AnalyzerGraph): boolean => {
 	}
 
 	// Check if this is a perfect elimination ordering
-	// For each vertex, its later neighbors should form a clique
-	const laterNeighbors = new Map<AnalyzerVertexId, Set<AnalyzerVertexId>>();
+	// For MCS, we check that for each vertex, its earlier neighbors form a clique
+	const earlierNeighbors = new Map<AnalyzerVertexId, Set<AnalyzerVertexId>>();
 
 	for (let index = 0; index < order.length; index++) {
 		const v = order[index];
-		const laterNbs = new Set<AnalyzerVertexId>();
+		const earlierNbs = new Set<AnalyzerVertexId>();
 
-		// Find neighbors that appear later in ordering
+		// Find neighbors that appear earlier in ordering
 		for (const nb of adj[v] ?? []) {
 			const index_ = order.indexOf(nb);
-			if (index_ > index) laterNbs.add(nb);
+			if (index_ < index) earlierNbs.add(nb);
 		}
 
-		laterNeighbors.set(v, laterNbs);
+		earlierNeighbors.set(v, earlierNbs);
 	}
 
-	// Check each set of later neighbors forms a clique
-	for (const [, laterNbs] of laterNeighbors) {
-		const nbs = [...laterNbs];
+	// Check each set of earlier neighbors forms a clique
+	for (const [, earlierNbs] of earlierNeighbors) {
+		const nbs = [...earlierNbs];
 		for (let index = 0; index < nbs.length; index++) {
 			for (let index_ = index + 1; index_ < nbs.length; index_++) {
 				// Check if nbs[i] and nbs[j] are adjacent

src/analyzer/types.ts

@@ -236,25 +236,25 @@ export const isChordalUndirectedBinary = (g: AnalyzerGraph): boolean => {
 	}
 
 	// Check if this is a perfect elimination ordering
-	// For each vertex, its later neighbors should form a clique
-	const laterNeighbors = new Map<AnalyzerVertexId, Set<AnalyzerVertexId>>();
+	// For MCS, we check that for each vertex, its earlier neighbors form a clique
+	const earlierNeighbors = new Map<AnalyzerVertexId, Set<AnalyzerVertexId>>();
 
 	for (let index = 0; index < order.length; index++) {
 		const v = order[index];
-		const laterNbs = new Set<AnalyzerVertexId>();
+		const earlierNbs = new Set<AnalyzerVertexId>();
 
-		// Find neighbors that appear later in ordering
+		// Find neighbors that appear earlier in ordering
 		for (const nb of adj[v] ?? []) {
 			const index_ = order.indexOf(nb);
-			if (index_ > index) laterNbs.add(nb);
+			if (index_ < index) earlierNbs.add(nb);
 		}
 
-		laterNeighbors.set(v, laterNbs);
+		earlierNeighbors.set(v, earlierNbs);
 	}
 
-	// Check each set of later neighbors forms a clique
-	for (const [, laterNbs] of laterNeighbors) {
-		const nbs = [...laterNbs];
+	// Check each set of earlier neighbors forms a clique
+	for (const [, earlierNbs] of earlierNeighbors) {
+		const nbs = [...earlierNbs];
 		for (let index = 0; index < nbs.length; index++) {
 			for (let index_ = index + 1; index_ < nbs.length; index_++) {
 				// Check if nbs[i] and nbs[j] are adjacent