diff --git a/app/assets/javascripts/pipelines/components/graph/graph_component.vue b/app/assets/javascripts/pipelines/components/graph/graph_component.vue
index a84161ef5e7..1f1b99ff401 100644
--- a/app/assets/javascripts/pipelines/components/graph/graph_component.vue
+++ b/app/assets/javascripts/pipelines/components/graph/graph_component.vue
@@ -64,6 +64,24 @@
       capitalizeStageName(name) {
         return name.charAt(0).toUpperCase() + name.slice(1);
       },
+
+      isFirstColumn(index) {
+        return index === 0;
+      },
+
+      stageConnectorClass(index, stage) {
+        let className;
+
+        // If it's the first stage column and only has one job
+        if (index === 0 && stage.groups.length === 1) {
+          className = 'no-margin';
+        } else if (index > 0) {
+          // If it is not the first column
+          className = 'left-margin';
+        }
+
+        return className;
+      },
     },
   };
 </script>
@@ -82,10 +100,12 @@
         v-if="!isLoading"
         class="stage-column-list">
         <stage-column-component
-          v-for="stage in state.graph"
+          v-for="(stage, index) in state.graph"
           :title="capitalizeStageName(stage.name)"
           :jobs="stage.groups"
-          :key="stage.name"/>
+          :key="stage.name"
+          :stage-connector-class="stageConnectorClass(index, stage)"
+          :is-first-column="isFirstColumn(index)"/>
       </ul>
     </div>
   </div>
diff --git a/app/assets/javascripts/pipelines/components/graph/stage_column_component.vue b/app/assets/javascripts/pipelines/components/graph/stage_column_component.vue
index b7da185e280..9b1bbb0906f 100644
--- a/app/assets/javascripts/pipelines/components/graph/stage_column_component.vue
+++ b/app/assets/javascripts/pipelines/components/graph/stage_column_component.vue
@@ -13,6 +13,18 @@ export default {
       type: Array,
       required: true,
     },
+
+    isFirstColumn: {
+      type: Boolean,
+      required: false,
+      default: false,
+    },
+
+    stageConnectorClass: {
+      type: String,
+      required: false,
+      default: '',
+    },
   },
 
   components: {
@@ -28,20 +40,27 @@ export default {
     jobId(job) {
       return `ci-badge-${job.name}`;
     },
+
+    buildConnnectorClass(index) {
+      return index === 0 && !this.isFirstColumn ? 'left-connector' : '';
+    },
   },
 };
 </script>
 <template>
-  <li class="stage-column">
+  <li
+    class="stage-column"
+    :class="stageConnectorClass">
     <div class="stage-name">
       {{title}}
     </div>
     <div class="builds-container">
       <ul>
         <li
-          v-for="job in jobs"
+          v-for="(job, index) in jobs"
           :key="job.id"
           class="build"
+          :class="buildConnnectorClass(index)"
           :id="jobId(job)">
 
           <div class="curve"></div>
diff --git a/app/assets/javascripts/vue_shared/ci_action_icons.js b/app/assets/javascripts/vue_shared/ci_action_icons.js
index 734b3c6c45e..ee41dc95beb 100644
--- a/app/assets/javascripts/vue_shared/ci_action_icons.js
+++ b/app/assets/javascripts/vue_shared/ci_action_icons.js
@@ -1,6 +1,7 @@
 import cancelSVG from 'icons/_icon_action_cancel.svg';
 import retrySVG from 'icons/_icon_action_retry.svg';
 import playSVG from 'icons/_icon_action_play.svg';
+import stopSVG from 'icons/_icon_action_stop.svg';
 
 export default function getActionIcon(action) {
   let icon;
@@ -14,6 +15,9 @@ export default function getActionIcon(action) {
     case 'icon_action_play':
       icon = playSVG;
       break;
+    case 'icon_action_stop':
+      icon = stopSVG;
+      break;
     default:
       icon = '';
   }
diff --git a/spec/javascripts/pipelines/graph/graph_component_spec.js b/spec/javascripts/pipelines/graph/graph_component_spec.js
index a756617e65e..77f42312b40 100644
--- a/spec/javascripts/pipelines/graph/graph_component_spec.js
+++ b/spec/javascripts/pipelines/graph/graph_component_spec.js
@@ -52,6 +52,56 @@ describe('graph component', () => {
                 },
               }],
             }],
+          },
+          {
+            name: 'test_1',
+            title: 'test_1: passed',
+            status: {
+              icon: 'icon_status_success',
+              text: 'passed',
+              label: 'passed',
+              details_path: '/root/ci-mock/pipelines/123#test',
+            },
+            path: '/root/ci-mock/pipelines/123#test',
+            groups: [{
+              name: 'test',
+              size: 1,
+              jobs: [{
+                id: 4153,
+                name: 'test',
+                status: {
+                  icon: 'icon_status_success',
+                  text: 'passed',
+                  label: 'passed',
+                  details_path: '/root/ci-mock/builds/4153',
+                  action: {
+                    icon: 'icon_action_retry',
+                    title: 'Retry',
+                    path: '/root/ci-mock/builds/4153/retry',
+                    method: 'post',
+                  },
+                },
+              }],
+            }, {
+              name: 'test',
+              size: 1,
+              jobs: [{
+                id: 4153,
+                name: 'test',
+                status: {
+                  icon: 'icon_status_success',
+                  text: 'passed',
+                  label: 'passed',
+                  details_path: '/root/ci-mock/builds/4153',
+                  action: {
+                    icon: 'icon_action_retry',
+                    title: 'Retry',
+                    path: '/root/ci-mock/builds/4153/retry',
+                    method: 'post',
+                  },
+                },
+              }],
+            }],
           }],
         },
       }), {
@@ -73,6 +123,18 @@ describe('graph component', () => {
       setTimeout(() => {
         expect(component.$el.classList.contains('js-pipeline-graph')).toEqual(true);
 
+        expect(
+          component.$el.querySelector('.stage-column:first-child').classList.contains('no-margin'),
+        ).toEqual(true);
+
+        expect(
+          component.$el.querySelector('.stage-column:nth-child(2)').classList.contains('left-margin'),
+        ).toEqual(true);
+
+        expect(
+          component.$el.querySelector('.stage-column:nth-child(2) .build:nth-child(1)').classList.contains('left-connector'),
+        ).toEqual(true);
+
         expect(component.$el.querySelector('loading-icon')).toBe(null);
 
         expect(component.$el.querySelector('.stage-column-list')).toBeDefined();
diff --git a/spec/javascripts/vue_shared/ci_action_icons_spec.js b/spec/javascripts/vue_shared/ci_action_icons_spec.js
index 2e89a07e76e..3d53a5ab24d 100644
--- a/spec/javascripts/vue_shared/ci_action_icons_spec.js
+++ b/spec/javascripts/vue_shared/ci_action_icons_spec.js
@@ -2,6 +2,7 @@ import getActionIcon from '~/vue_shared/ci_action_icons';
 import cancelSVG from 'icons/_icon_action_cancel.svg';
 import retrySVG from 'icons/_icon_action_retry.svg';
 import playSVG from 'icons/_icon_action_play.svg';
+import stopSVG from 'icons/_icon_action_stop.svg';
 
 describe('getActionIcon', () => {
   it('should return an empty string', () => {
@@ -19,4 +20,8 @@ describe('getActionIcon', () => {
   it('should return play svg', () => {
     expect(getActionIcon('icon_action_play')).toEqual(playSVG);
   });
+
+  it('should render stop svg', () => {
+    expect(getActionIcon('icon_action_stop')).toEqual(stopSVG);
+  });
 });