diff --git a/src/analysis/index.ts b/src/analysis/index.ts
index 4083db8..68cf0dc 100644
--- a/src/analysis/index.ts
+++ b/src/analysis/index.ts
@@ -4,8 +4,7 @@ export {
   defaultEdgeType,
   resolveDefaultNodeAttrs,
 } from "./defaults.js";
-export { typeCompat, type TypeCompatResult, type TypeMismatch } from "./type-compat.js";
-export { buildTypeEdges } from "../graph/construction.js";
+export { typeCompat, buildTypeEdges, type TypeCompatResult, type TypeMismatch } from "./type-compat.js";
 export {
   validateSchema,
   validateGraph,
diff --git a/src/analysis/type-compat.ts b/src/analysis/type-compat.ts
index ed36cb0..018c9e1 100644
--- a/src/analysis/type-compat.ts
+++ b/src/analysis/type-compat.ts
@@ -1,4 +1,11 @@
 import { KindGuard, Kind, type TSchema } from "@alkdev/typebox";
+import { willCreateCycle } from "graphology-dag";
+import type { FlowGraph } from "../graph/construction.js";
+import {
+  OperationNodeAttrs as OperationNodeAttrsSchema,
+  OperationEdgeAttrs as OperationEdgeAttrsSchema,
+} from "../schema/index.js";
+import type { OperationNodeAttrs } from "../schema/index.js";
 
 export interface TypeMismatch {
   path: string;
@@ -275,4 +282,25 @@ export function typeCompat(outputSchema: TSchema, inputSchema: TSchema): TypeCom
   }
 
   return { compatible: false, mismatches };
+}
+
+export function buildTypeEdges(graph: FlowGraph<typeof OperationNodeAttrsSchema, typeof OperationEdgeAttrsSchema>): void {
+  const nodeKeys = graph.nodes();
+  for (const source of nodeKeys) {
+    for (const target of nodeKeys) {
+      if (source === target) continue;
+      const sourceAttrs = graph.getNodeAttributes(source as never) as unknown as OperationNodeAttrs;
+      const targetAttrs = graph.getNodeAttributes(target as never) as unknown as OperationNodeAttrs;
+      const result = typeCompat(sourceAttrs.outputSchema as TSchema, targetAttrs.inputSchema as TSchema);
+      if (result === undefined) continue;
+      if (graph.hasEdge(source, target)) continue;
+      if (willCreateCycle(graph.graph, source, target)) continue;
+      const detail = result.detail ?? `${sourceAttrs.namespace}.${sourceAttrs.name}.output → ${targetAttrs.namespace}.${targetAttrs.name}.input`;
+      graph.addTypedEdge(source, target, {
+        compatible: result.compatible,
+        detail,
+        ...(result.mismatches !== undefined ? { mismatches: result.mismatches } : {}),
+      });
+    }
+  }
 }
\ No newline at end of file
diff --git a/src/graph/construction.ts b/src/graph/construction.ts
index 3f8b6dd..96e3837 100644
--- a/src/graph/construction.ts
+++ b/src/graph/construction.ts
@@ -21,8 +21,10 @@ import {
   OperationGraphSerialized,
   CallGraphSerialized,
 } from "../schema/index.js";
-import type { OperationNodeAttrs, FlowGraphSerialized } from "../schema/index.js";
-import { typeCompat, type TypeCompatResult } from "../analysis/type-compat.js";
+import type { FlowGraphSerialized } from "../schema/index.js";
+import { buildTypeEdges, type TypeCompatResult } from "../analysis/type-compat.js";
+
+export { buildTypeEdges } from "../analysis/type-compat.js";
 
 export interface FlowGraphOptions {
   type?: "directed";
@@ -455,25 +457,4 @@ export class FlowGraph<
     }
     return [];
   }
-}
-
-export function buildTypeEdges(graph: OperationGraph): void {
-  const nodeKeys = graph.nodes();
-  for (const source of nodeKeys) {
-    for (const target of nodeKeys) {
-      if (source === target) continue;
-      const sourceAttrs = graph.getNodeAttributes(source as never) as unknown as OperationNodeAttrs;
-      const targetAttrs = graph.getNodeAttributes(target as never) as unknown as OperationNodeAttrs;
-      const result = typeCompat(sourceAttrs.outputSchema as TSchema, targetAttrs.inputSchema as TSchema);
-      if (result === undefined) continue;
-      if (graph.hasEdge(source, target)) continue;
-      if (willCreateCycle(graph.graph, source, target)) continue;
-      const detail = result.detail ?? `${sourceAttrs.namespace}.${sourceAttrs.name}.output → ${targetAttrs.namespace}.${targetAttrs.name}.input`;
-      graph.addTypedEdge(source, target, {
-        compatible: result.compatible,
-        detail,
-        ...(result.mismatches !== undefined ? { mismatches: result.mismatches } : {}),
-      });
-    }
-  }
 }
\ No newline at end of file
diff --git a/src/index.ts b/src/index.ts
index 37319a2..a7e44e8 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -1,6 +1,7 @@
 export * from "./error/index.js";
 
 export { FlowGraph, buildTypeEdges, type FlowGraphOptions, type OperationSpec } from "./graph/index.js";
+export { typeCompat, type TypeCompatResult, type TypeMismatch } from "./analysis/type-compat.js";
 export {
   validateSchema,
   validateGraph,
diff --git a/test/analysis/type-compat.test.ts b/test/analysis/type-compat.test.ts
index 1d8b072..237b263 100644
--- a/test/analysis/type-compat.test.ts
+++ b/test/analysis/type-compat.test.ts
@@ -1,6 +1,8 @@
 import { describe, it, expect } from "vitest";
 import { Type, type TSchema } from "@alkdev/typebox";
-import { typeCompat, type TypeCompatResult, type TypeMismatch } from "../../src/analysis/type-compat.js";
+import { typeCompat, buildTypeEdges, type TypeCompatResult, type TypeMismatch } from "../../src/analysis/type-compat.js";
+import { FlowGraph } from "../../src/graph/construction.js";
+import type { OperationSpec } from "../../src/graph/construction.js";
 
 describe("typeCompat", () => {
   describe("exact match", () => {
@@ -411,4 +413,111 @@ describe("typeCompat", () => {
       expect(typeof mismatch.actual).toBe("string");
     });
   });
+});
+
+describe("buildTypeEdges", () => {
+  it("adds compatible edges for matching output→input schemas", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "extract", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ raw: Type.String() }), outputSchema: Type.Object({ text: Type.String() }) });
+    fg.addOperation({ name: "classify", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ text: Type.String() }), outputSchema: Type.Object({ label: Type.String(), score: Type.Number() }) });
+    buildTypeEdges(fg);
+    expect(fg.hasEdge("task.extract", "task.classify")).toBe(true);
+    const attrs = fg.getEdgeAttributes("task.extract", "task.classify") as Record<string, unknown>;
+    expect(attrs.edgeType).toBe("typed");
+    expect(attrs.compatible).toBe(true);
+  });
+
+  it("adds incompatible edges when schemas mismatch", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "classify", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ text: Type.String() }), outputSchema: Type.Object({ label: Type.String(), score: Type.Number() }) });
+    fg.addOperation({ name: "count", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ count: Type.Number() }), outputSchema: Type.Object({ result: Type.Number() }) });
+    buildTypeEdges(fg);
+    expect(fg.hasEdge("task.classify", "task.count")).toBe(true);
+    const attrs = fg.getEdgeAttributes("task.classify", "task.count") as Record<string, unknown>;
+    expect(attrs.edgeType).toBe("typed");
+    expect(attrs.compatible).toBe(false);
+    expect(attrs.mismatches).toBeDefined();
+  });
+
+  it("incompatible edges include mismatches array", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "a", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ x: Type.String() }), outputSchema: Type.Object({ value: Type.String() }) });
+    fg.addOperation({ name: "b", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ value: Type.Number() }), outputSchema: Type.Object({ z: Type.Boolean() }) });
+    buildTypeEdges(fg);
+    const attrs = fg.getEdgeAttributes("op.a", "op.b") as Record<string, unknown>;
+    expect(attrs.compatible).toBe(false);
+    expect(Array.isArray(attrs.mismatches)).toBe(true);
+    expect((attrs.mismatches as Array<unknown>).length).toBeGreaterThan(0);
+  });
+
+  it("does not add edges when either schema is Unknown", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "unk_out", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ x: Type.String() }), outputSchema: Type.Unknown() });
+    fg.addOperation({ name: "unk_in", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Unknown(), outputSchema: Type.Object({ y: Type.String() }) });
+    fg.addOperation({ name: "normal", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ y: Type.String() }), outputSchema: Type.Object({ x: Type.String() }) });
+    buildTypeEdges(fg);
+    expect(fg.hasEdge("op.unk_out", "op.unk_in")).toBe(false);
+    expect(fg.hasEdge("op.unk_out", "op.normal")).toBe(false);
+    expect(fg.hasEdge("op.normal", "op.unk_in")).toBe(false);
+  });
+
+  it("sets detail to namespace.name.output → namespace.name.input for compatible edges", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "extract", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ raw: Type.String() }), outputSchema: Type.Object({ text: Type.String() }) });
+    fg.addOperation({ name: "classify", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ text: Type.String() }), outputSchema: Type.Object({ label: Type.String() }) });
+    buildTypeEdges(fg);
+    const attrs = fg.getEdgeAttributes("task.extract", "task.classify") as Record<string, unknown>;
+    expect(attrs.detail).toContain("task.extract.output → task.classify.input");
+  });
+
+  it("is callable after incremental addOperation calls", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "extract", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ raw: Type.String() }), outputSchema: Type.Object({ text: Type.String() }) });
+    buildTypeEdges(fg);
+    expect(fg.size).toBe(0);
+    fg.addOperation({ name: "classify", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ text: Type.String() }), outputSchema: Type.Object({ label: Type.String() }) });
+    buildTypeEdges(fg);
+    expect(fg.hasEdge("op.extract", "op.classify")).toBe(true);
+  });
+
+  it("produces edges for three operations in a pipeline", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "extract", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ raw: Type.String() }), outputSchema: Type.Object({ text: Type.String() }) });
+    fg.addOperation({ name: "classify", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ text: Type.String() }), outputSchema: Type.Object({ label: Type.String() }) });
+    fg.addOperation({ name: "enrich", namespace: "task", version: "1.0.0", type: "query", inputSchema: Type.Object({ label: Type.String() }), outputSchema: Type.Object({ enriched: Type.String() }) });
+    buildTypeEdges(fg);
+    expect(fg.hasEdge("task.extract", "task.classify")).toBe(true);
+    expect(fg.hasEdge("task.classify", "task.enrich")).toBe(true);
+    expect(fg.hasEdge("task.extract", "task.enrich")).toBe(true);
+    const e2c = fg.getEdgeAttributes("task.extract", "task.classify") as Record<string, unknown>;
+    const c2e = fg.getEdgeAttributes("task.classify", "task.enrich") as Record<string, unknown>;
+    const e2e = fg.getEdgeAttributes("task.extract", "task.enrich") as Record<string, unknown>;
+    expect(e2c.compatible).toBe(true);
+    expect(c2e.compatible).toBe(true);
+    expect(e2e.compatible).toBe(false);
+  });
+
+  it("does not add self-loops", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "a", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ x: Type.String() }), outputSchema: Type.Object({ x: Type.String() }) });
+    buildTypeEdges(fg);
+    expect(fg.size).toBe(0);
+  });
+
+  it("returns empty graph with no edges for empty graph", () => {
+    const fg = new FlowGraph();
+    buildTypeEdges(fg);
+    expect(fg.order).toBe(0);
+    expect(fg.size).toBe(0);
+  });
+
+  it("skips edges that would already exist", () => {
+    const fg = new FlowGraph();
+    fg.addOperation({ name: "a", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ x: Type.String() }), outputSchema: Type.Object({ y: Type.String() }) });
+    fg.addOperation({ name: "b", namespace: "op", version: "1.0.0", type: "query", inputSchema: Type.Object({ y: Type.String() }), outputSchema: Type.Object({ z: Type.String() }) });
+    buildTypeEdges(fg);
+    const sizeAfterFirst = fg.size;
+    buildTypeEdges(fg);
+    expect(fg.size).toBe(sizeAfterFirst);
+  });
 });
\ No newline at end of file