diff --git a/pkg/gui/presentation/graph/cell.go b/pkg/gui/presentation/graph/cell.go
index 618a2149d..5660c5745 100644
--- a/pkg/gui/presentation/graph/cell.go
+++ b/pkg/gui/presentation/graph/cell.go
@@ -21,17 +21,33 @@ const (
 	MERGE
 )
 
+// How a line that touches the top or bottom edge of a cell runs within it
+type verticalLine uint8
+
+const (
+	noLine verticalLine = iota
+	// On to the opposite edge, or into the commit symbol
+	straightLine
+	// Bends towards the left edge
+	lineToLeft
+	// Bends towards the right edge
+	lineToRight
+)
+
 type Cell struct {
-	up, down, left, right bool
-	cellType              cellType
-	rightStyle            *style.TextStyle
-	style                 *style.TextStyle
+	// The lines that touch the top and bottom edges
+	up, down verticalLine
+	// Whether lines touch the left and right edges
+	left, right bool
+	// Whether a line passes through from the left edge to the right edge
+	horizontal bool
+	cellType   cellType
+	rightStyle *style.TextStyle
+	style      *style.TextStyle
 }
 
 func (cell *Cell) render(writer io.StringWriter) {
-	up, down, left, right := cell.up, cell.down, cell.left, cell.right
-
-	first, second := getBoxDrawingChars(up, down, left, right)
+	first, second := getBoxDrawingChars(cell.up != noLine, cell.down != noLine, cell.left, cell.right)
 	var adjustedFirst string
 	switch cell.cellType {
 	case CONNECTION:
@@ -98,34 +114,34 @@ func cachedSprint(style style.TextStyle, str string) string {
 }
 
 func (cell *Cell) reset() {
-	cell.up = false
-	cell.down = false
+	cell.up = noLine
+	cell.down = noLine
 	cell.left = false
 	cell.right = false
+	cell.horizontal = false
 }
 
-func (cell *Cell) setUp(style *style.TextStyle) *Cell {
-	cell.up = true
+func (cell *Cell) setUp(style *style.TextStyle, line verticalLine) *Cell {
+	cell.up = line
 	cell.style = style
 	return cell
 }
 
-func (cell *Cell) setDown(style *style.TextStyle) *Cell {
-	cell.down = true
+func (cell *Cell) setDown(style *style.TextStyle, line verticalLine) *Cell {
+	cell.down = line
 	cell.style = style
 	return cell
 }
 
 func (cell *Cell) setLeft(style *style.TextStyle) *Cell {
 	cell.left = true
-	if !cell.up && !cell.down {
+	if cell.up == noLine && cell.down == noLine {
 		// vertical trumps left
 		cell.style = style
 	}
 	return cell
 }
 
-//nolint:unparam
 func (cell *Cell) setRight(style *style.TextStyle, override bool) *Cell {
 	cell.right = true
 	if cell.rightStyle == nil || override {
@@ -134,6 +150,11 @@ func (cell *Cell) setRight(style *style.TextStyle, override bool) *Cell {
 	return cell
 }
 
+func (cell *Cell) setHorizontal(style *style.TextStyle, overrideRightStyle bool) *Cell {
+	cell.horizontal = true
+	return cell.setLeft(style).setRight(style, overrideRightStyle)
+}
+
 func (cell *Cell) setStyle(style *style.TextStyle) *Cell {
 	cell.style = style
 	return cell
diff --git a/pkg/gui/presentation/graph/graph.go b/pkg/gui/presentation/graph/graph.go
index c267bbbcb..996892d7b 100644
--- a/pkg/gui/presentation/graph/graph.go
+++ b/pkg/gui/presentation/graph/graph.go
@@ -303,17 +303,17 @@ func renderPipeSet(
 
 		if left != right {
 			for i := left + 1; i < right; i++ {
-				cells[i].setLeft(style).setRight(style, overrideRightStyle)
+				cells[i].setHorizontal(style, overrideRightStyle)
 			}
 			cells[left].setRight(style, overrideRightStyle)
 			cells[right].setLeft(style)
 		}
 
 		if pipe.kind == STARTS || pipe.kind == CONTINUES {
-			cells[pipe.toPos].setDown(style)
+			cells[pipe.toPos].setDown(style, lineTowards(pipe.toPos, pipe.fromPos))
 		}
 		if pipe.kind == TERMINATES || pipe.kind == CONTINUES {
-			cells[pipe.fromPos].setUp(style)
+			cells[pipe.fromPos].setUp(style, lineTowards(pipe.fromPos, pipe.toPos))
 		}
 	}
 
@@ -375,6 +375,19 @@ func renderPipeSet(
 	return writer.String()
 }
 
+// The course of a line through the top or bottom edge of the cell at pos,
+// given the column of the pipe's other end
+func lineTowards(pos, otherPos int16) verticalLine {
+	switch {
+	case otherPos < pos:
+		return lineToLeft
+	case otherPos > pos:
+		return lineToRight
+	default:
+		return straightLine
+	}
+}
+
 func equalHashes(a, b *string) bool {
 	// if our selectedCommitHashPtr is nil, there is no selected commit
 	if a == nil || b == nil {