diff --git a/dvc/repo/index.py b/dvc/repo/index.py
index a3f789c37..a86805c3f 100644
--- a/dvc/repo/index.py
+++ b/dvc/repo/index.py
@@ -11,7 +11,7 @@ from typing import (
     Set,
 )
 
-from funcy import cached_property, memoize, nullcontext
+from funcy import cached_property, nullcontext
 
 from dvc.utils import dict_md5
 
@@ -146,9 +146,11 @@ class Index:
 
         return build_outs_trie(self.stages)
 
-    @property
+    @cached_property
     def graph(self) -> "DiGraph":
-        return self.build_graph()
+        from dvc.repo.graph import build_graph
+
+        return build_graph(self.stages, self.outs_trie)
 
     @cached_property
     def outs_graph(self) -> "DiGraph":
@@ -230,15 +232,9 @@ class Index:
             stages.remove(stage)
         return stages
 
-    @memoize
-    def build_graph(self) -> "DiGraph":
-        from dvc.repo.graph import build_graph
-
-        return build_graph(self.stages, self.outs_trie)
-
     def check_graph(self) -> None:
         if not getattr(self.repo, "_skip_graph_checks", False):
-            self.build_graph()
+            self.graph  # pylint: disable=pointless-statement
 
     def dumpd(self) -> Dict[str, Dict]:
         def dump(stage: "Stage"):
@@ -275,7 +271,7 @@ if __name__ == "__main__":
         # pylint: disable=pointless-statement
         print("no of stages", len(index.stages))
     with log_durations(print, "building graph"):
-        index.build_graph()
+        index.graph  # pylint: disable=pointless-statement
     with log_durations(print, "calculating hash"):
         print(index.identifier)
     with log_durations(print, "updating"):
diff --git a/tests/func/test_repo_index.py b/tests/func/test_repo_index.py
index e6d1eb7c6..22826a78c 100644
--- a/tests/func/test_repo_index.py
+++ b/tests/func/test_repo_index.py
@@ -24,7 +24,6 @@ def test_index(tmp_dir, scm, dvc, run_copy):
 
     assert index.outs_graph
     assert index.graph
-    assert index.build_graph()
     assert isinstance(index.outs_trie, Trie)
     assert index.identifier
     index.check_graph()
@@ -229,7 +228,7 @@ def test_unique_identifier(tmp_dir, dvc, scm, run_copy):
 
 def test_skip_graph_checks(dvc, mocker):
     # See https://github.com/iterative/dvc/issues/2671 for more info
-    mock_build_graph = mocker.spy(Index, "build_graph")
+    mock_build_graph = mocker.spy(Index.graph, "fget")
 
     # sanity check
     Index(dvc).check_graph()
diff --git a/tests/unit/repo/test_repo.py b/tests/unit/repo/test_repo.py
index ce519bbf6..1528ca6ba 100644
--- a/tests/unit/repo/test_repo.py
+++ b/tests/unit/repo/test_repo.py
@@ -77,7 +77,9 @@ def test_locked(mocker):
 
 def test_skip_graph_checks(tmp_dir, dvc, mocker, run_copy):
     # See https://github.com/iterative/dvc/issues/2671 for more info
-    mock_build_graph = mocker.patch("dvc.repo.index.Index.build_graph")
+    from dvc.repo.index import Index
+
+    mock_build_graph = mocker.spy(Index.graph, "fget")
 
     # sanity check
     tmp_dir.gen("foo", "foo text")