diff --git a/src/graph/graph.hh b/src/graph/graph.hh
index c6f088499..79119c626 100644
--- a/src/graph/graph.hh
+++ b/src/graph/graph.hh
@@ -49,6 +49,48 @@ struct graph_t
     unsigned end = 0;
     unsigned priority = 0;
 
+
+    bool link_positions_valid (unsigned num_objects)
+    {
+      hb_set_t assigned_bytes;
+      for (const auto& l : obj.real_links)
+      {
+        if (l.objidx >= num_objects)
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Invalid object index.");
+          return false;
+        }
+
+        unsigned start = l.position;
+        unsigned end = start + l.width - 1;
+
+        if (unlikely (l.width < 2 || l.width > 4))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Invalid link width.");
+          return false;
+        }
+
+        if (unlikely (end >= table_size ()))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Link position is out of bounds.");
+          return false;
+        }
+
+        if (unlikely (assigned_bytes.intersects (start, end)))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Found offsets whose positions overlap.");
+          return false;
+        }
+
+        assigned_bytes.add_range (start, end);
+      }
+      return true;
+    }
+
     void normalize ()
     {
       obj.real_links.qsort ();
@@ -286,8 +328,6 @@ struct graph_t
     vertices_scratch_.alloc (objects.length);
     for (unsigned i = 0; i < objects.length; i++)
     {
-      // TODO(grieger): check all links point to valid objects.
-
       // If this graph came from a serialization buffer object 0 is the
       // nil object. We don't need it for our purposes here so drop it.
       if (i == 0 && !objects[i])
@@ -299,6 +339,9 @@ struct graph_t
       vertex_t* v = vertices_.push ();
       if (check_success (!vertices_.in_error ()))
         v->obj = *objects[i];
+
+      check_success (v->link_positions_valid (objects.length));
+
       if (!removed_nil) continue;
       // Fix indices to account for removed nil object.
       for (auto& l : v->obj.all_links_writer ()) {
@@ -418,6 +461,13 @@ struct graph_t
       hb_swap (sorted_graph[new_id], vertices_[next_id]);
       const vertex_t& next = sorted_graph[new_id];
 
+      if (unlikely (!check_success(new_id >= 0))) {
+        // We are out of ids. Which means we've visited a node more than once.
+        // This graph contains a cycle which is not allowed.
+        DEBUG_MSG (SUBSET_REPACK, nullptr, "Invalid graph. Contains cycle.");
+        return;
+      }
+
       id_map[next_id] = new_id--;
 
       for (const auto& link : next.obj.all_links ()) {
@@ -941,6 +991,72 @@ struct graph_t
     return made_change;
   }
 
+  bool is_fully_connected ()
+  {
+    update_parents();
+
+    if (root().parents)
+      // Root cannot have parents.
+      return false;
+
+    for (unsigned i = 0; i < root_idx (); i++)
+    {
+      if (!vertices_[i].parents)
+        return false;
+    }
+    return true;
+  }
+
+#if 0
+  /*
+   * Saves the current graph to a packed binary format which the repacker fuzzer takes
+   * as a seed.
+   */
+  void save_fuzzer_seed (hb_tag_t tag) const
+  {
+    FILE* f = fopen ("./repacker_fuzzer_seed", "w");
+    fwrite ((void*) &tag, sizeof (tag), 1, f);
+
+    uint16_t num_objects = vertices_.length;
+    fwrite ((void*) &num_objects, sizeof (num_objects), 1, f);
+
+    for (const auto& v : vertices_)
+    {
+      uint16_t blob_size = v.table_size ();
+      fwrite ((void*) &blob_size, sizeof (blob_size), 1, f);
+      fwrite ((const void*) v.obj.head, blob_size, 1, f);
+    }
+
+    uint16_t link_count = 0;
+    for (const auto& v : vertices_)
+      link_count += v.obj.real_links.length;
+
+    fwrite ((void*) &link_count, sizeof (link_count), 1, f);
+
+    typedef struct
+    {
+      uint16_t parent;
+      uint16_t child;
+      uint16_t position;
+      uint8_t width;
+    } link_t;
+
+    for (unsigned i = 0; i < vertices_.length; i++)
+    {
+      for (const auto& l : vertices_[i].obj.real_links)
+      {
+        link_t link {
+          (uint16_t) i, (uint16_t) l.objidx,
+          (uint16_t) l.position, (uint8_t) l.width
+        };
+        fwrite ((void*) &link, sizeof (link), 1, f);
+      }
+    }
+
+    fclose (f);
+  }
+#endif
+
   void print_orphaned_nodes ()
   {
     if (!DEBUG_ENABLED(SUBSET_REPACK)) return;
@@ -949,6 +1065,10 @@ struct graph_t
     parents_invalid = true;
     update_parents();
 
+    if (root().parents) {
+      DEBUG_MSG (SUBSET_REPACK, nullptr, "Root node has incoming edges.");
+    }
+
     for (unsigned i = 0; i < root_idx (); i++)
     {
       const auto& v = vertices_[i];
diff --git a/src/hb-repacker.hh b/src/hb-repacker.hh
index 70f1d0e08..6817ffae4 100644
--- a/src/hb-repacker.hh
+++ b/src/hb-repacker.hh
@@ -283,6 +283,11 @@ hb_resolve_graph_overflows (hb_tag_t table_tag,
                             graph_t& sorted_graph /* IN/OUT */)
 {
   sorted_graph.sort_shortest_distance ();
+  if (sorted_graph.in_error ())
+  {
+    DEBUG_MSG (SUBSET_REPACK, nullptr, "Sorted graph in error state after initial sort.");
+    return false;
+  }
 
   bool will_overflow = graph::will_overflow (sorted_graph);
   if (!will_overflow)
@@ -376,6 +381,18 @@ hb_resolve_overflows (const T& packed,
                       unsigned max_rounds = 20,
                       bool recalculate_extensions = false) {
   graph_t sorted_graph (packed);
+  if (sorted_graph.in_error ())
+  {
+    // Invalid graph definition.
+    return nullptr;
+  }
+
+  if (!sorted_graph.is_fully_connected ())
+  {
+    sorted_graph.print_orphaned_nodes ();
+    return nullptr;
+  }
+
   if (!hb_resolve_graph_overflows (table_tag, max_rounds, recalculate_extensions, sorted_graph))
     return nullptr;
 
diff --git a/src/test-repacker.cc b/src/test-repacker.cc
index 7a20ba52c..94ff0849a 100644
--- a/src/test-repacker.cc
+++ b/src/test-repacker.cc
@@ -1476,6 +1476,7 @@ static void test_sort_shortest ()
 
   graph_t graph (c.object_graph ());
   graph.sort_shortest_distance ();
+  assert (!graph.in_error ());
 
   assert(strncmp (graph.object (4).head, "abc", 3) == 0);
   assert(graph.object (4).real_links.length == 3);
diff --git a/test/fuzzing/graphs/crash-3bf72494aa4c9f8cbbcbf887fdc2a2858c87feb4 b/test/fuzzing/graphs/crash-3bf72494aa4c9f8cbbcbf887fdc2a2858c87feb4
new file mode 100644
index 000000000..ff8da7b29
Binary files /dev/null and b/test/fuzzing/graphs/crash-3bf72494aa4c9f8cbbcbf887fdc2a2858c87feb4 differ
diff --git a/test/fuzzing/graphs/crash-442bfac994a3d9929cf06262ae9fb00f6ee1f774 b/test/fuzzing/graphs/crash-442bfac994a3d9929cf06262ae9fb00f6ee1f774
new file mode 100644
index 000000000..0160ce59b
Binary files /dev/null and b/test/fuzzing/graphs/crash-442bfac994a3d9929cf06262ae9fb00f6ee1f774 differ
diff --git a/test/fuzzing/graphs/leak-a77f29b25edb873729f3ab120148fdb213cfa527 b/test/fuzzing/graphs/leak-a77f29b25edb873729f3ab120148fdb213cfa527
new file mode 100644
index 000000000..58b4075ad
Binary files /dev/null and b/test/fuzzing/graphs/leak-a77f29b25edb873729f3ab120148fdb213cfa527 differ
diff --git a/test/fuzzing/graphs/noto_nastaliq_urdu b/test/fuzzing/graphs/noto_nastaliq_urdu
new file mode 100644
index 000000000..2e3cab886
Binary files /dev/null and b/test/fuzzing/graphs/noto_nastaliq_urdu differ
diff --git a/test/fuzzing/hb-repacker-fuzzer.cc b/test/fuzzing/hb-repacker-fuzzer.cc
new file mode 100644
index 000000000..536b0e8d0
--- /dev/null
+++ b/test/fuzzing/hb-repacker-fuzzer.cc
@@ -0,0 +1,145 @@
+#include "hb-fuzzer.hh"
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <assert.h>
+
+#include "hb-subset-repacker.h"
+
+typedef struct
+{
+  uint16_t parent;
+  uint16_t child;
+  uint16_t position;
+  uint8_t width;
+} link_t;
+
+/* The fuzzer seed contains a serialized representation of a object graph which forms
+ * the input graph to the repacker call. The binary format is:
+ *
+ * table tag: 4 bytes
+ * number of objects: 2 bytes
+ * objects[number of objects]:
+ *   blob size: 2 bytes
+ *   blob: blob size bytes
+ * num of real links: 2 bytes
+ * links[number of real links]: link_t struct
+ *
+ * TODO(garretrieger): add optional virtual links
+ */
+
+template <typename T>
+bool read(const uint8_t** data, size_t* size, T* out)
+{
+  if (*size < sizeof (T)) return false;
+
+  *out = * ((T*) *data);
+
+  *data += sizeof (T);
+  *size -= sizeof (T);
+
+  return true;
+}
+
+void cleanup (hb_object_t* objects, uint16_t num_objects)
+{
+  for (uint32_t i = 0; i < num_objects; i++)
+  {
+    free (objects[i].head);
+    free (objects[i].real_links);
+  }
+}
+
+void add_links_to_objects (hb_object_t* objects, uint16_t num_objects,
+                           link_t* links, uint16_t num_links)
+{
+  unsigned* link_count = (unsigned*) calloc (num_objects, sizeof (unsigned));
+
+  for (uint32_t i = 0; i < num_links; i++)
+  {
+    uint16_t parent_idx = links[i].parent;
+    link_count[parent_idx]++;
+  }
+
+  for (uint32_t i = 0; i < num_objects; i++)
+  {
+    objects[i].num_real_links = link_count[i];
+    objects[i].real_links = (hb_link_t*) calloc (link_count[i], sizeof (hb_link_t));
+    objects[i].num_virtual_links = 0;
+    objects[i].virtual_links = nullptr;
+  }
+
+  for (uint32_t i = 0; i < num_links; i++)
+  {
+    uint16_t parent_idx = links[i].parent;
+    uint16_t child_idx = links[i].child + 1; // All indices are shifted by 1 by the null object.
+    hb_link_t* link = &(objects[parent_idx].real_links[link_count[parent_idx] - 1]);
+
+    link->width = links[i].width;
+    link->position = links[i].position;
+    link->objidx = child_idx;
+    link_count[parent_idx]--;
+  }
+
+  free (link_count);
+}
+
+extern "C" int LLVMFuzzerTestOneInput (const uint8_t *data, size_t size)
+{
+  // TODO(garretrieger): move graph validity checks into repacker graph creation.
+  alloc_state = _fuzzing_alloc_state (data, size);
+
+  uint16_t num_objects = 0;
+  hb_object_t* objects = nullptr;
+
+  uint16_t num_real_links = 0;
+  link_t* links = nullptr;
+
+  hb_tag_t table_tag;
+  if (!read<hb_tag_t> (&data, &size, &table_tag)) goto end;
+  if (!read<uint16_t> (&data, &size, &num_objects)) goto end;
+
+  objects = (hb_object_t*) calloc (num_objects, sizeof (hb_object_t));
+  for (uint32_t i = 0; i < num_objects; i++)
+  {
+    uint16_t blob_size;
+    if (!read<uint16_t> (&data, &size, &blob_size)) goto end;
+    if (size < blob_size) goto end;
+
+    char* copy = (char*) calloc (1, blob_size);
+    memcpy (copy, data, blob_size);
+    objects[i].head = (char*) copy;
+    objects[i].tail = (char*) (copy + blob_size);
+
+    size -= blob_size;
+    data += blob_size;
+  }
+
+  if (!read<uint16_t> (&data, &size, &num_real_links)) goto end;
+  links = (link_t*) calloc (num_real_links, sizeof (link_t));
+  for (uint32_t i = 0; i < num_real_links; i++)
+  {
+    if (!read<link_t> (&data, &size, &links[i])) goto end;
+
+    if (links[i].parent >= num_objects)
+      goto end;
+  }
+
+  add_links_to_objects (objects, num_objects,
+                        links, num_real_links);
+
+  hb_blob_destroy (hb_subset_repack_or_fail (table_tag,
+                                             objects,
+                                             num_objects));
+
+end:
+  if (objects)
+  {
+    cleanup (objects, num_objects);
+    free (objects);
+  }
+  free (links);
+
+  return 0;
+}
diff --git a/test/fuzzing/meson.build b/test/fuzzing/meson.build
index 3aba9eb67..d38ca8f9f 100644
--- a/test/fuzzing/meson.build
+++ b/test/fuzzing/meson.build
@@ -5,6 +5,10 @@ tests = [
   'hb-draw-fuzzer.cc',
 ]
 
+if get_option('experimental_api')
+  tests += 'hb-repacker-fuzzer.cc'
+endif
+
 foreach file_name : tests
   test_name = file_name.split('.')[0]
 
@@ -19,6 +23,10 @@ foreach file_name : tests
     extra_cpp_args += '-DHB_IS_IN_FUZZER'
   endif
 
+  if get_option('experimental_api')
+    extra_cpp_args += '-DHB_EXPERIMENTAL_API'
+  endif
+
   exe = executable(test_name, sources,
     cpp_args: cpp_args + extra_cpp_args,
     include_directories: [incconfig, incsrc],
@@ -55,6 +63,20 @@ test('subset_fuzzer', find_program('run-subset-fuzzer-tests.py'),
   suite: ['fuzzing', 'slow'],
 )
 
+if get_option('experimental_api')
+  test('repacker_fuzzer', find_program('run-repacker-fuzzer-tests.py'),
+    args: [
+      hb_repacker_fuzzer_exe,
+    ],
+    # as the tests are ran concurrently let's raise acceptable time here
+    # ideally better to break and let meson handles them in parallel
+    timeout: 300,
+    workdir: meson.current_build_dir() / '..' / '..',
+    env: env,
+    suite: ['fuzzing', 'slow'],
+  )
+endif
+
 test('draw_fuzzer', find_program('run-draw-fuzzer-tests.py'),
   args: [
     hb_draw_fuzzer_exe,
diff --git a/test/fuzzing/run-repacker-fuzzer-tests.py b/test/fuzzing/run-repacker-fuzzer-tests.py
new file mode 100644
index 000000000..85a23e13e
--- /dev/null
+++ b/test/fuzzing/run-repacker-fuzzer-tests.py
@@ -0,0 +1,68 @@
+#!/usr/bin/env python3
+
+import sys, os, subprocess, tempfile, shutil
+
+
+def cmd (command):
+	# https://stackoverflow.com/a/4408409 as we might have huge output sometimes
+	with tempfile.TemporaryFile () as tempf:
+		p = subprocess.Popen (command, stderr=tempf)
+
+		try:
+			p.wait ()
+			tempf.seek (0)
+			text = tempf.read ()
+
+			#TODO: Detect debug mode with a better way
+			is_debug_mode = b"SANITIZE" in text
+
+			return ("" if is_debug_mode else text.decode ("utf-8").strip ()), p.returncode
+		except subprocess.TimeoutExpired:
+			return 'error: timeout, ' + ' '.join (command), 1
+
+
+srcdir = os.getenv ("srcdir", ".")
+EXEEXT = os.getenv ("EXEEXT", "")
+top_builddir = os.getenv ("top_builddir", ".")
+hb_repacker_fuzzer = os.path.join (top_builddir, "hb-repacker-fuzzer" + EXEEXT)
+
+if not os.path.exists (hb_repacker_fuzzer):
+        if len (sys.argv) < 2 or not os.path.exists (sys.argv[1]):
+                sys.exit ("""Failed to find hb-repacker-fuzzer binary automatically,
+please provide it as the first argument to the tool""")
+
+        hb_repacker_fuzzer = sys.argv[1]
+
+print ('hb_repacker_fuzzer:', hb_repacker_fuzzer)
+fails = 0
+
+valgrind = None
+if os.getenv ('RUN_VALGRIND', ''):
+	valgrind = shutil.which ('valgrind')
+	if valgrind is None:
+		sys.exit ("""Valgrind requested but not found.""")
+
+def run_dir (parent_path):
+	global fails
+	for file in os.listdir (parent_path):
+		path = os.path.join(parent_path, file)
+		print ("running repacker fuzzer against %s" % path)
+		if valgrind:
+			text, returncode = cmd ([valgrind, '--leak-check=full', '--error-exitcode=1', hb_repacker_fuzzer, path])
+		else:
+			text, returncode = cmd ([hb_repacker_fuzzer, path])
+			if 'error' in text:
+				returncode = 1
+
+		if (not valgrind or returncode) and text.strip ():
+			print (text)
+
+		if returncode != 0:
+			print ("failed for %s" % path)
+			fails = fails + 1
+
+
+run_dir (os.path.join (srcdir, "graphs"))
+
+if fails:
+	sys.exit ("%d repacker fuzzer related tests failed." % fails)