diff --git a/src/canvas/edge.test.ts b/src/canvas/edge.test.ts
new file mode 100644
index 0000000..cbe5670
--- /dev/null
+++ b/src/canvas/edge.test.ts
@@ -0,0 +1,16 @@
+import Edge from "./edge";
+import edge from "./edge";
+
+describe("id", () => {
+test("should create an id from an edge", () => {
+    const edge = { sourceId: "1", targetId: "2" };
+    expect(Edge.id(edge)).toEqual("1-->2");
+  });
+});
+
+describe("parseId", () => {
+  test("should return an edge from an id", () => {
+    const id = "1-->2";
+    expect(Edge.parseId(id)).toEqual({ sourceId: "1", targetId: "2" });
+  });
+});
diff --git a/src/canvas/edge.ts b/src/canvas/edge.ts
index 201413a..e77b827 100644
--- a/src/canvas/edge.ts
+++ b/src/canvas/edge.ts
@@ -3,6 +3,13 @@ interface Edge {
   targetId: string;
 }
 
+const ArrowSymbol = "-->";
+
 export default {
-  id: (edge: Edge): string => `${edge.sourceId}-->${edge.targetId}`,
+  id: (edge: Edge): string => `${edge.sourceId}${ArrowSymbol}${edge.targetId}`,
+
+  parseId: (edgeId: string): Edge => {
+    const [sourceId, targetId] = edgeId.split(ArrowSymbol);
+    return { sourceId, targetId };
+  },
 };
diff --git a/src/interface/control.ts b/src/interface/control.ts
index 8959708..01e9bba 100644
--- a/src/interface/control.ts
+++ b/src/interface/control.ts
@@ -3,7 +3,7 @@ import { html } from "htm/react";
 import { Store } from "redux";
 
 import { ApplicationState } from "../store";
-import { deleteAtom, evalSelectedAtom } from "../store/defaultReducer";
+import { deleteAtom, evalSelectedAtom, deleteEdge } from "../store/defaultReducer";
 import { selectors as canvasSelectors } from "../canvas";
 import PlayIcon from "./play_icon";
 import TrashIcon from "./trash_icon";
@@ -11,7 +11,7 @@ import CastIcon from "./cast_icon";
 import BookIcon from "./book_icon";
 import { actions } from "./interfaceReducer";
 
-const { getSelectedAtomId } = canvasSelectors;
+const { getSelectedAtomId, getSelectedEdgeId } = canvasSelectors;
 const { toggleTranscript } = actions;
 
 interface Props {
@@ -20,10 +20,12 @@ interface Props {
 
 export default function Control({ store }: Props) {
   const [selectedAtomId, setSelectedAtomId] = useState(null);
+  const [selectedEdgeId, setSelectedEdgeId] = useState(null);
   const [connectedToRepl, setConnectedToRepl] = useState(false);
 
   store.subscribe(() => {
     setSelectedAtomId(getSelectedAtomId(store.getState()));
+    setSelectedEdgeId(getSelectedEdgeId(store.getState()));
     setConnectedToRepl(store.getState().default.connectedToRepl);
   });
 
@@ -36,7 +38,8 @@ export default function Control({ store }: Props) {
   const onDeleteClick = (event) => {
     event.preventDefault();
     event.stopPropagation();
-    store.dispatch(deleteAtom(selectedAtomId));
+    if (selectedAtomId) store.dispatch(deleteAtom(selectedAtomId));
+    if (selectedEdgeId) store.dispatch(deleteEdge(selectedEdgeId));
   }
 
   const onTranscriptClick = (event) => {
@@ -58,7 +61,7 @@ export default function Control({ store }: Props) {
         <${PlayIcon} />
       </button>
       <button className="control-button"
-              disabled=${!selectedAtomId}
+              disabled=${!selectedAtomId && !selectedEdgeId}
               onClick=${onDeleteClick}>
         <${TrashIcon} />
       </button>
diff --git a/src/keyboard/index.ts b/src/keyboard/index.ts
index 8d2cf4e..33fe955 100644
--- a/src/keyboard/index.ts
+++ b/src/keyboard/index.ts
@@ -2,7 +2,7 @@ import * as Mousetrap from "mousetrap";
 import { ApplicationState } from "../store";
 import {
   deleteAtom as deleteAtomAction, addAtom, connectAtoms, childrenSelector,
-  evalSelectedAtom, parentSelector, deepChildrenSelector
+  evalSelectedAtom, parentSelector, deepChildrenSelector, deleteEdge
 } from "../store/defaultReducer";
 import { buildNodeGeometry } from "../canvas/node_geometry";
 import { createAtom } from "../store/atom";
@@ -16,30 +16,44 @@ import { remote } from "electron";
 const { dialog } = remote;
 const { select, unselect, changeMode } = actions;
 const { toggleTranscript } = interfaceActions;
-const { getSelectedAtom, getMode } = selectors;
+const { getSelectedAtom, getMode, getSelectedEdgeId } = selectors;
 
 export default function Keyboard(store: Store<ApplicationState>) {
   let state = store.getState();
   let mode = getMode(store.getState());
   let selectedAtom = getSelectedAtom(store.getState());
+  let selectedEdgeId = getSelectedEdgeId(store.getState());
 
   store.subscribe(() => {
     state = store.getState();
     mode = getMode(store.getState());
     selectedAtom = getSelectedAtom(store.getState());
+    selectedEdgeId = getSelectedEdgeId(store.getState());
   });
 
   const standardAtomOffset = 40;
   const evaluateAtom = () => store.dispatch(evalSelectedAtom());
-  const deleteAtom = (event) => {
-    if (!selectedAtom) return;
-
-    event.preventDefault();
 
+  const deleteSelectedAtom = () => {
     const parent = parentSelector(state.default, selectedAtom.id);
     store.dispatch(deleteAtomAction(selectedAtom.id));
     if (parent) store.dispatch(select(parent.id));
   };
+
+  const deleteSelectedEdge = () => store.dispatch(deleteEdge(selectedEdgeId));
+
+  const deleteSelectedElement = (event) => {
+    if (selectedAtom) {
+      event.preventDefault();
+      deleteSelectedAtom();
+    }
+
+    if (selectedEdgeId) {
+      event.preventDefault();
+      deleteSelectedEdge();
+    }
+  };
+
   const createChildAtom = (event) => {
     if (!selectedAtom) return;
 
@@ -163,7 +177,7 @@ export default function Keyboard(store: Store<ApplicationState>) {
   };
 
   Mousetrap.bind("command+e", evaluateAtom);
-  Mousetrap.bind("command+backspace", deleteAtom);
+  Mousetrap.bind("command+backspace", deleteSelectedElement);
   Mousetrap.bind("tab", createChildAtom);
   Mousetrap.bind("command+enter", handleCmdEnter);
   Mousetrap.bind("esc", handleEsc);
diff --git a/src/store/defaultReducer.ts b/src/store/defaultReducer.ts
index 0847b41..f07b584 100644
--- a/src/store/defaultReducer.ts
+++ b/src/store/defaultReducer.ts
@@ -5,6 +5,7 @@ import { buildNodeGeometry } from "../canvas/node_geometry";
 import { Line } from "../canvas/geometry";
 import { ApplicationState } from ".";
 import { EvalResult } from "../repl";
+import Edge from "../canvas/edge";
 
 export interface DefaultState {
   atoms: { [id: string]: Atom };
@@ -43,6 +44,10 @@ export const setAtomValue =
 export const evalSelectedAtom =
   () => ({ type: "eval-selected-atom" });
 
+export const deleteEdge = (edgeId: string) => (
+  { type: "delete-edge", payload: Edge.parseId(edgeId) }
+);
+
 const initialState: DefaultState = {
   atoms: {},
   edges: [],
@@ -66,6 +71,12 @@ const reducer = createReducer(initialState, {
       return !isSource && !isTarget;
     });
   },
+  "delete-edge": (state, action) => {
+    const notMatchingEdge = (signature) => ({ sourceId, targetId }) => (
+      !(sourceId === signature.sourceId && targetId === signature.targetId)
+    );
+    state.edges = state.edges.filter(notMatchingEdge(action.payload));
+  },
   "add-atom": (state, action) => {
     state.atoms[action.payload.id] = action.payload;
   },