diff --git a/src/index.ts b/src/index.ts
index f79127a..18e85e2 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -1,4 +1,5 @@
 import { JSONSchema, JSONSchemaObject, PatternProperties } from "@json-schema-tools/meta-schema";
+import { jsonPathStringify, isCycle, last } from "./utils";
 
 /**
  * Signature of the mutation method passed to traverse.
@@ -49,28 +50,6 @@ export const defaultOptions: TraverseOptions = {
   bfs: false,
 };
 
-const jsonPathStringify = (s: string[]) => {
-  return s.map((i) => {
-    if (i === "") {
-      return '$';
-    } else {
-      return `.${i}`;
-    }
-  }).join("");
-};
-
-const isCycle = (s: JSONSchema, recursiveStack: JSONSchema[]): JSONSchema | false => {
-  const foundInRecursiveStack = recursiveStack.find((recSchema) => recSchema === s);
-  if (foundInRecursiveStack) {
-    return foundInRecursiveStack;
-  }
-  return false;
-};
-
-const last = (i: JSONSchema[], skip = 1): JSONSchema => {
-  return i[i.length - skip];
-};
-
 /**
  * Traverse all subschema of a schema, calling the mutator function with each.
  * The mutator is called on leaf nodes first.
@@ -273,11 +252,11 @@ export default function traverse(
     mutableStack.pop();
     return mutableSchema;
   } else {
-    const isCycle = cycleSet.indexOf(schema) !== -1
+    const isCycleNode = cycleSet.indexOf(schema) !== -1
     mutableStack.pop();
     return mutation(
       mutableSchema,
-      isCycle,
+      isCycleNode,
       jsonPathStringify(pathStack),
       last(mutableStack)
     );
diff --git a/src/utils.ts b/src/utils.ts
new file mode 100644
index 0000000..eb6e29e
--- /dev/null
+++ b/src/utils.ts
@@ -0,0 +1,28 @@
+import { JSONSchema } from "@json-schema-tools/meta-schema";
+
+export const jsonPathStringify = (s: string[]): string => {
+  return s
+    .map((i) => {
+      if (i === "") {
+        return "$";
+      } else {
+        return `.${i}`;
+      }
+    })
+    .join("");
+};
+
+export const isCycle = (
+  s: JSONSchema,
+  recursiveStack: JSONSchema[],
+): JSONSchema | false => {
+  const foundInRecursiveStack = recursiveStack.find((recSchema) => recSchema === s);
+  if (foundInRecursiveStack) {
+    return foundInRecursiveStack;
+  }
+  return false;
+};
+
+export const last = (i: JSONSchema[], skip = 1): JSONSchema => {
+  return i[i.length - skip];
+};