diff --git a/graph/path/yen_ksp.go b/graph/path/yen_ksp.go
index 04f6e50c..82b1b808 100644
--- a/graph/path/yen_ksp.go
+++ b/graph/path/yen_ksp.go
@@ -85,7 +85,18 @@ func YenKShortestPaths(g graph.Graph, k int, cost float64, s, t graph.Node) [][]
 				spath = append(root[:len(root)-1], spath...)
 				weight += rootWeight
 			}
-			pot = append(pot, yenShortest{spath, weight})
+
+			// Add the potential k-shortest path if it is new.
+			isNewPot := true
+			for x := range pot {
+				if isSamePath(pot[x].path, spath) {
+					isNewPot = false
+					break
+				}
+			}
+			if isNewPot {
+				pot = append(pot, yenShortest{spath, weight})
+			}
 		}
 
 		if len(pot) == 0 {
@@ -104,6 +115,19 @@ func YenKShortestPaths(g graph.Graph, k int, cost float64, s, t graph.Node) [][]
 	return paths
 }
 
+func isSamePath(a, b []graph.Node) bool {
+	if len(a) != len(b) {
+		return false
+	}
+
+	for i, x := range a {
+		if x.ID() != b[i].ID() {
+			return false
+		}
+	}
+	return true
+}
+
 // yenShortest holds a path and its weight for sorting.
 type yenShortest struct {
 	path   []graph.Node
diff --git a/graph/path/yen_ksp_test.go b/graph/path/yen_ksp_test.go
index eabf4a91..70702c66 100644
--- a/graph/path/yen_ksp_test.go
+++ b/graph/path/yen_ksp_test.go
@@ -306,6 +306,28 @@ var yenShortestPathTests = []struct {
 			{8, 2, 4, 3, 7, 5},
 		},
 	},
+	{
+		name:  "grid", // This is the failing case in gonum/gonum#1920.
+		graph: func() graph.WeightedEdgeAdder { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
+		edges: []simple.WeightedEdge{
+			{F: simple.Node(1), T: simple.Node(2), W: 1},
+			{F: simple.Node(2), T: simple.Node(3), W: 2},
+			{F: simple.Node(3), T: simple.Node(6), W: 5},
+			{F: simple.Node(1), T: simple.Node(4), W: 5},
+			{F: simple.Node(2), T: simple.Node(5), W: 4},
+			{F: simple.Node(4), T: simple.Node(5), W: 6},
+			{F: simple.Node(5), T: simple.Node(6), W: 7},
+		},
+		query: simple.Edge{F: simple.Node(1), T: simple.Node(6)},
+		k:     -1,
+		cost:  math.Inf(1),
+		wantPaths: [][]int64{
+			{1, 2, 3, 6},
+			{1, 2, 5, 6},
+			{1, 4, 5, 6},
+			{1, 4, 5, 2, 3, 6},
+		},
+	},
 }
 
 func bipartite(n int, weight, inc float64) []simple.WeightedEdge {