diff --git a/src/backend/graph.js b/src/backend/graph.js
index 16873e0..351b2a9 100644
--- a/src/backend/graph.js
+++ b/src/backend/graph.js
@@ -70,10 +70,17 @@ export class Graph {
     if (node == null) {
       throw new Error(`node is ${String(node)}`);
     }
-    if (this.getNode(node.address) !== undefined) {
-      throw new Error(
-        `node at address ${JSON.stringify(node.address)} already exists`
-      );
+    const existingNode = this.getNode(node.address);
+    if (existingNode !== undefined) {
+      if (deepEqual(existingNode, node)) {
+        return this;
+      } else {
+        throw new Error(
+          `node at address ${JSON.stringify(
+            node.address
+          )} exists with distinct contents`
+        );
+      }
     }
     this._nodes.add(node);
     this._outEdges.add({address: node.address, edges: []});
@@ -85,10 +92,17 @@ export class Graph {
     if (edge == null) {
       throw new Error(`edge is ${String(edge)}`);
     }
-    if (this.getEdge(edge.address) !== undefined) {
-      throw new Error(
-        `edge at address ${JSON.stringify(edge.address)} already exists`
-      );
+    const existingEdge = this.getEdge(edge.address);
+    if (existingEdge !== undefined) {
+      if (deepEqual(existingEdge, edge)) {
+        return this;
+      } else {
+        throw new Error(
+          `edge at address ${JSON.stringify(
+            edge.address
+          )} exists with distinct contents`
+        );
+      }
     }
     if (this.getNode(edge.src) === undefined) {
       throw new Error(`source ${JSON.stringify(edge.src)} does not exist`);
diff --git a/src/backend/graph.test.js b/src/backend/graph.test.js
index 0af5ea0..3224300 100644
--- a/src/backend/graph.test.js
+++ b/src/backend/graph.test.js
@@ -192,24 +192,36 @@ describe("graph", () => {
     });
 
     describe("creating nodes and edges", () => {
-      it("forbids adding a node with existing address", () => {
+      it("forbids adding a node with existing address and different contents", () => {
         expect(() =>
           demoData.simpleMealGraph().addNode({
             address: demoData.crabNode().address,
             payload: {anotherCrab: true},
           })
-        ).toThrow(/already exists/);
+        ).toThrow(/exists with distinct contents/);
       });
 
-      it("forbids adding an edge with existing address", () => {
+      it("adding a node redundantly is a no-op", () => {
+        const simple1 = demoData.simpleMealGraph();
+        const simple2 = demoData.simpleMealGraph().addNode(demoData.heroNode());
+        expect(simple1.equals(simple2)).toBe(true);
+      });
+
+      it("forbids adding an edge with existing address and different contents", () => {
         expect(() =>
           demoData.simpleMealGraph().addEdge({
             address: demoData.cookEdge().address,
             src: demoData.crabNode().address,
             dst: demoData.crabNode().address,
-            payload: {},
+            payload: {isDifferent: true},
           })
-        ).toThrow(/already exists/);
+        ).toThrow(/exists with distinct contents/);
+      });
+
+      it("adding an edge redundantly is a no-op", () => {
+        const simple1 = demoData.simpleMealGraph();
+        const simple2 = demoData.simpleMealGraph().addEdge(demoData.cookEdge());
+        expect(simple1.equals(simple2)).toBe(true);
       });
 
       it("allows creating self-loops", () => {