diff --git a/src/data-structures/graph/GraphVertex.js b/src/data-structures/graph/GraphVertex.js
index 34be0fc5..7389e6e6 100644
--- a/src/data-structures/graph/GraphVertex.js
+++ b/src/data-structures/graph/GraphVertex.js
@@ -9,10 +9,22 @@ export default class GraphVertex {
       throw new Error('Graph vertex must have a value');
     }
 
+    /**
+     * @param {GraphEdge} edgeA
+     * @param {GraphEdge} edgeB
+     */
+    const edgeComparator = (edgeA, edgeB) => {
+      if (edgeA.getKey() === edgeB.getKey()) {
+        return 0;
+      }
+
+      return edgeA.getKey() < edgeB.getKey() ? -1 : 1;
+    };
+
     // Normally you would store string value like vertex name.
     // But generally it may be any object as well
     this.value = value;
-    this.edges = new LinkedList();
+    this.edges = new LinkedList(edgeComparator);
   }
 
   /**
@@ -25,6 +37,13 @@ export default class GraphVertex {
     return this;
   }
 
+  /**
+   * @param {GraphEdge} edge
+   */
+  deleteEdge(edge) {
+    this.edges.delete(edge);
+  }
+
   /**
    * @returns {GraphVertex[]}
    */
diff --git a/src/data-structures/graph/__test__/GraphVertex.test.js b/src/data-structures/graph/__test__/GraphVertex.test.js
index 8512c34d..1610e377 100644
--- a/src/data-structures/graph/__test__/GraphVertex.test.js
+++ b/src/data-structures/graph/__test__/GraphVertex.test.js
@@ -37,6 +37,39 @@ describe('GraphVertex', () => {
     expect(vertexA.getEdges()[0].toString()).toBe('A_B');
   });
 
+  it('should delete edges from vertex', () => {
+    const vertexA = new GraphVertex('A');
+    const vertexB = new GraphVertex('B');
+    const vertexC = new GraphVertex('C');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB);
+    const edgeAC = new GraphEdge(vertexA, vertexC);
+    vertexA
+      .addEdge(edgeAB)
+      .addEdge(edgeAC);
+
+    expect(vertexA.hasEdge(edgeAB)).toBeTruthy();
+    expect(vertexB.hasEdge(edgeAB)).toBeFalsy();
+
+    expect(vertexA.hasEdge(edgeAC)).toBeTruthy();
+    expect(vertexC.hasEdge(edgeAC)).toBeFalsy();
+
+    expect(vertexA.getEdges().length).toBe(2);
+
+    expect(vertexA.getEdges()[0].toString()).toBe('A_B');
+    expect(vertexA.getEdges()[1].toString()).toBe('A_C');
+
+    vertexA.deleteEdge(edgeAB);
+    expect(vertexA.hasEdge(edgeAB)).toBeFalsy();
+    expect(vertexA.hasEdge(edgeAC)).toBeTruthy();
+    expect(vertexA.getEdges()[0].toString()).toBe('A_C');
+
+    vertexA.deleteEdge(edgeAC);
+    expect(vertexA.hasEdge(edgeAB)).toBeFalsy();
+    expect(vertexA.hasEdge(edgeAC)).toBeFalsy();
+    expect(vertexA.getEdges().length).toBe(0);
+  });
+
   it('should return vertex neighbors in case if current node is start one', () => {
     const vertexA = new GraphVertex('A');
     const vertexB = new GraphVertex('B');
diff --git a/src/data-structures/linked-list/LinkedList.js b/src/data-structures/linked-list/LinkedList.js
index 0835d85a..b428ad73 100644
--- a/src/data-structures/linked-list/LinkedList.js
+++ b/src/data-structures/linked-list/LinkedList.js
@@ -67,13 +67,15 @@ export default class LinkedList {
 
     let currentNode = this.head;
 
-    // If next node must be deleted then make next node to be a next next one.
-    while (currentNode.next) {
-      if (this.compare.equal(currentNode.next.value, value)) {
-        deletedNode = currentNode.next;
-        currentNode.next = currentNode.next.next;
-      } else {
-        currentNode = currentNode.next;
+    if (currentNode !== null) {
+      // If next node must be deleted then make next node to be a next next one.
+      while (currentNode.next) {
+        if (this.compare.equal(currentNode.next.value, value)) {
+          deletedNode = currentNode.next;
+          currentNode.next = currentNode.next.next;
+        } else {
+          currentNode = currentNode.next;
+        }
       }
     }
 
diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index e400a0ea..1b938e1b 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -67,6 +67,9 @@ describe('LinkedList', () => {
 
     expect(linkedList.head.toString()).toBe('2');
     expect(linkedList.tail.toString()).toBe('2');
+
+    linkedList.delete(2);
+    expect(linkedList.toString()).toBe('');
   });
 
   it('should delete linked list tail', () => {