diff --git a/frontend/src/lib/components/assets/AssetGraph/AssetGraphCanvas.svelte b/frontend/src/lib/components/assets/AssetGraph/AssetGraphCanvas.svelte
index 4e2ef0bdcb..c0b8dff779 100644
--- a/frontend/src/lib/components/assets/AssetGraph/AssetGraphCanvas.svelte
+++ b/frontend/src/lib/components/assets/AssetGraph/AssetGraphCanvas.svelte
@@ -28,6 +28,7 @@
 		type AssetUpstreamDelete
 	} from './assetsOnlyView'
 	import { assetsOnlyNodeWidth } from './assetNodeWidth'
+	import { describeEdge } from './edgeDescription'
 	import { isAssetsOnlyFolder, setAssetsOnlyFolder } from './assetsOnlyFolders'
 	import { formatAssetKind, formatShortAssetPath } from '$lib/components/assets/lib'
 	import { TRIGGER_NODE_STYLE } from './TriggerNode.svelte'
@@ -267,6 +268,34 @@
 	// Right-click on the empty canvas: a menu at the pointer whose entry opens the
 	// add-data-source menu there too.
 	let paneMenu = $state<{ x: number; y: number } | undefined>(undefined)
+
+	// Hovering an edge names the relationship it draws, after a short pause so
+	// sweeping the pointer across the canvas doesn't flash popovers.
+	let hoveredEdge = $state<{ id: string; x: number; y: number } | undefined>(undefined)
+	let edgeHoverTimer: ReturnType<typeof setTimeout> | undefined
+	function onEdgeEnter({ edge, event }: { edge: Edge; event: PointerEvent }) {
+		clearTimeout(edgeHoverTimer)
+		const at = { id: edge.id, x: event.clientX, y: event.clientY }
+		edgeHoverTimer = setTimeout(() => (hoveredEdge = at), 300)
+	}
+	function onEdgeLeave() {
+		clearTimeout(edgeHoverTimer)
+		hoveredEdge = undefined
+	}
+	let hoveredEdgeText = $derived.by(() => {
+		const e = hoveredEdge && view.edges.find((x) => x.id === hoveredEdge!.id)
+		if (!e) return undefined
+		const byId = new Map(view.nodes.map((n) => [n.id, n]))
+		const nameOf = (id: string) => {
+			const n = byId.get(id)
+			if (!n) return id.replace(/^[^:]+:/, '')
+			if (n.type === 'asset') return formatShortAssetPath({ kind: n.data.asset_kind, path: n.data.path })
+			if (n.type === 'no-asset') return 'the scripts that build no asset'
+			if (n.type === 'trigger') return n.data.summary || n.data.ref
+			return n.data.summary || n.data.path
+		}
+		return describeEdge(e, nameOf, (id) => byId.get(id)?.data)
+	})
 	let addMenuAt = $state<{ x: number; y: number }>({ x: 0, y: 0 })
 	let addMenuSignal = $state(0)
 	function handleContextMenu(e: MouseEvent) {
@@ -332,6 +361,8 @@
 		// whole lib when pulled in via `// use`) — rendered as a ƒ badge.
 		macro_names?: string[]
 		via_use?: boolean
+		// Assets-only edges: the scripts folded between the two assets.
+		via?: string[]
 	}
 
 	// Graph-id of the script the user just launched (zero-latency hint),
@@ -1635,6 +1666,8 @@
 		defaultEdgeOptions={{ type: 'asset' }}
 		proOptions={{ hideAttribution: true }}
 		onnodeclick={handleNodeClick}
+		onedgepointerenter={onEdgeEnter}
+		onedgepointerleave={onEdgeLeave}
 		--background-color={false}
 	>
 		<div class="absolute inset-0 !bg-surface-secondary h-full"></div>
@@ -1719,6 +1752,21 @@
 	</div>
 {/if}
 
+{#if hoveredEdge && hoveredEdgeText}
+	{@const d = hoveredEdgeText}
+	<div
+		class="fixed z-50 max-w-80 rounded-md border bg-surface px-2.5 py-1.5 text-xs text-primary shadow-md pointer-events-none"
+		style="left: {hoveredEdge.x + 12}px; top: {hoveredEdge.y + 12}px;"
+		transition:fly={{ duration: 120, y: -4 }}
+		role="tooltip"
+	>
+		<span class="font-semibold text-emphasis">{d.subject}</span>
+		{d.phrase}
+		{#if d.object}<span class="font-semibold text-emphasis">{d.object}</span>{/if}
+		{#if d.note}<div class="mt-0.5 text-2xs text-secondary">{d.note}</div>{/if}
+	</div>
+{/if}
+
 {#if onAddPipelineScript}
 	<div class="fixed w-0 h-0" style="left: {addMenuAt.x}px; top: {addMenuAt.y}px;">
 		<AddDataSourceMenu
diff --git a/frontend/src/lib/components/assets/AssetGraph/AssetGraphEdge.svelte b/frontend/src/lib/components/assets/AssetGraph/AssetGraphEdge.svelte
index d7be5b15e6..90825986b8 100644
--- a/frontend/src/lib/components/assets/AssetGraph/AssetGraphEdge.svelte
+++ b/frontend/src/lib/components/assets/AssetGraph/AssetGraphEdge.svelte
@@ -179,7 +179,7 @@
 	path={edgePath}
 	{markerEnd}
 	{style}
-	interactionWidth={0}
+	interactionWidth={12}
 	label={undefined}
 	labelStyle={undefined}
 />
diff --git a/frontend/src/lib/components/assets/AssetGraph/assetsOnlyView.ts b/frontend/src/lib/components/assets/AssetGraph/assetsOnlyView.ts
index e5efea9ac1..0cef27f8c6 100644
--- a/frontend/src/lib/components/assets/AssetGraph/assetsOnlyView.ts
+++ b/frontend/src/lib/components/assets/AssetGraph/assetsOnlyView.ts
@@ -8,6 +8,8 @@ export type ViewEdge = {
 	target: string
 	kind: string
 	unsaved?: boolean
+	/** Assets-only edges: the folded runnables the data goes through. */
+	via?: string[]
 }
 
 /** The assets-only node standing for the scripts that build no asset. */
@@ -70,8 +72,19 @@ export function assetsOnlyView<N extends ViewNode, E extends ViewEdge>(
 				const id = `flow:${r.source}->${assetId}`
 				const prev = out.get(id)
 				const unsaved = !!(w.unsaved || r.unsaved)
-				if (prev) prev.unsaved = prev.unsaved && unsaved
-				else out.set(id, { id, source: r.source, target: assetId, kind: 'asset-flow', unsaved })
+				if (prev) {
+					prev.unsaved = prev.unsaved && unsaved
+					if (!prev.via?.includes(w.source)) prev.via = [...(prev.via ?? []), w.source]
+				} else {
+					out.set(id, {
+						id,
+						source: r.source,
+						target: assetId,
+						kind: 'asset-flow',
+						unsaved,
+						via: [w.source]
+					})
+				}
 			}
 		}
 	}
@@ -123,15 +136,19 @@ export function assetsOnlyView<N extends ViewNode, E extends ViewEdge>(
 			for (const r of inputsOf.get(id) ?? []) {
 				const eid = `flow:${r.source}->${NO_ASSET_NODE_ID}`
 				const prev = out.get(eid)
-				if (prev) prev.unsaved = prev.unsaved && !!r.unsaved
-				else
+				if (prev) {
+					prev.unsaved = prev.unsaved && !!r.unsaved
+					if (!prev.via?.includes(id)) prev.via = [...(prev.via ?? []), id]
+				} else {
 					out.set(eid, {
 						id: eid,
 						source: r.source,
 						target: NO_ASSET_NODE_ID,
 						kind: 'asset-flow',
-						unsaved: !!r.unsaved
+						unsaved: !!r.unsaved,
+						via: [id]
 					})
+				}
 			}
 		}
 	}
diff --git a/frontend/src/lib/components/assets/AssetGraph/edgeDescription.test.ts b/frontend/src/lib/components/assets/AssetGraph/edgeDescription.test.ts
new file mode 100644
index 0000000000..093daf11d0
--- /dev/null
+++ b/frontend/src/lib/components/assets/AssetGraph/edgeDescription.test.ts
@@ -0,0 +1,51 @@
+import { describe, expect, it } from 'vitest'
+import { describeEdge } from './edgeDescription'
+
+const names: Record<string, string> = {
+	'asset:ducklake:main/raw': 'raw',
+	'asset:ducklake:main/clean': 'clean',
+	'script:f/p/clean': 'Clean',
+	'trigger:schedule:f/p/daily': 'Daily'
+}
+const nameOf = (id: string) => names[id] ?? id
+const dataOf = (id: string) =>
+	id === 'trigger:schedule:f/p/daily'
+		? { kind: 'schedule', schedule: '0 0 12 * * *', timezone: 'UTC' }
+		: undefined
+
+describe('describeEdge', () => {
+	it('names an asset trigger by what runs it: any write, changed or not', () => {
+		expect(
+			describeEdge(
+				{ source: 'asset:ducklake:main/raw', target: 'script:f/p/clean', kind: 'trigger-asset' },
+				nameOf,
+				dataOf
+			)
+		).toEqual({ subject: 'Clean', phrase: 'runs after each write to', object: 'raw' })
+	})
+
+	it("gives a schedule's cadence", () => {
+		expect(
+			describeEdge(
+				{ source: 'trigger:schedule:f/p/daily', target: 'script:f/p/clean', kind: 'trigger-native' },
+				nameOf,
+				dataOf
+			)?.phrase
+		).toBe('runs on schedule: Every day at 12:00 UTC')
+	})
+
+	it('names the folded script on an assets-only edge', () => {
+		expect(
+			describeEdge(
+				{
+					source: 'asset:ducklake:main/raw',
+					target: 'asset:ducklake:main/clean',
+					kind: 'asset-flow',
+					via: ['script:f/p/clean']
+				},
+				nameOf,
+				dataOf
+			)
+		).toEqual({ subject: 'raw', phrase: 'feeds', object: 'clean', note: 'Via Clean.' })
+	})
+})
diff --git a/frontend/src/lib/components/assets/AssetGraph/edgeDescription.ts b/frontend/src/lib/components/assets/AssetGraph/edgeDescription.ts
new file mode 100644
index 0000000000..7093fb0ade
--- /dev/null
+++ b/frontend/src/lib/components/assets/AssetGraph/edgeDescription.ts
@@ -0,0 +1,96 @@
+import { describeSchedule } from '$lib/utils/describeCron'
+
+/** What a hovered edge says: "`subject` `phrase` `object`", then a note. */
+export type EdgeDescription = { subject: string; phrase: string; object?: string; note?: string }
+
+/** The edge fields the description reads (the canvas model's edge). */
+export type DescribedEdge = {
+	source: string
+	target: string
+	kind: string
+	unsaved?: boolean
+	muted?: boolean
+	missing?: boolean
+	via?: string[]
+	macro_names?: string[]
+	via_use?: boolean
+}
+
+// What starts a script, per trigger kind: "runs on <event>".
+const TRIGGER_EVENT: Record<string, string> = {
+	kafka: 'Kafka message',
+	mqtt: 'MQTT message',
+	amqp: 'AMQP message',
+	nats: 'NATS message',
+	sqs: 'SQS message',
+	gcp: 'Pub/Sub message',
+	email: 'incoming email',
+	postgres: 'Postgres event',
+	webhook: 'webhook call',
+	data_upload: 'data upload'
+}
+
+/**
+ * The relationship an edge draws, as a sentence about its two ends. `nameOf`
+ * names a node, `dataOf` gives its data (a trigger's kind and cadence).
+ */
+export function describeEdge(
+	e: DescribedEdge,
+	nameOf: (id: string) => string,
+	dataOf: (id: string) => any
+): EdgeDescription | undefined {
+	const src = nameOf(e.source)
+	const tgt = nameOf(e.target)
+	const draft = e.unsaved ? 'Not deployed yet.' : undefined
+	switch (e.kind) {
+		case 'lineage-write':
+			return { subject: src, phrase: 'writes to', object: tgt, note: draft }
+		case 'lineage-read':
+			return {
+				subject: tgt,
+				phrase: 'reads from',
+				object: src,
+				note: e.muted ? 'A write to it does not run the script (muted).' : draft
+			}
+		case 'trigger-asset':
+			return { subject: tgt, phrase: 'runs after each write to', object: src, note: draft }
+		case 'trigger-native': {
+			const t = dataOf(e.source) ?? {}
+			if (e.missing) {
+				return {
+					subject: tgt,
+					phrase: `declares \`// on ${t.kind}\`, but no trigger of that kind targets it`
+				}
+			}
+			const phrase =
+				t.kind === 'schedule' && t.schedule
+					? `runs on schedule: ${describeSchedule(t.schedule, t.timezone) ?? t.schedule}`
+					: `runs on ${TRIGGER_EVENT[t.kind] ?? `${t.kind} trigger`}`
+			return { subject: tgt, phrase, note: t.draft ? 'Draft trigger, created on save.' : draft }
+		}
+		case 'asset-flow': {
+			const via = (e.via ?? []).map(nameOf).join(', ')
+			return { subject: src, phrase: 'feeds', object: tgt, note: via ? `Via ${via}.` : undefined }
+		}
+		case 'dbt-ref':
+			return { subject: tgt, phrase: 'references', object: src, note: 'dbt ref().' }
+		case 'macro':
+			return {
+				subject: tgt,
+				phrase: e.via_use ? 'uses the macro library' : 'uses macros from',
+				object: src,
+				note: e.macro_names?.length ? e.macro_names.join(', ') : undefined
+			}
+		case 'test-dependency':
+			return {
+				subject: src,
+				phrase: 'must run before',
+				object: tgt,
+				note: 'Its data test reads what the first one builds.'
+			}
+		case 'data-test':
+			return { subject: tgt, phrase: 'tests', object: src }
+		default:
+			return undefined
+	}
+}