diff --git a/6103.fix.md b/6103.fix.md
new file mode 100644
index 00000000000..47844cd1ea6
--- /dev/null
+++ b/6103.fix.md
@@ -0,0 +1,2 @@
+Absolute dependencies (dependencies on tasks in a specified cycle rather than at a specified offset) are now visible in the GUI beyond the specified cycle.
+
diff --git a/cylc/flow/taskdef.py b/cylc/flow/taskdef.py
index 68f754277d8..448844c8cc3 100644
--- a/cylc/flow/taskdef.py
+++ b/cylc/flow/taskdef.py
@@ -101,11 +101,7 @@ def generate_graph_parents(tdef, point, taskdefs):
                 # where (point -Px) does not land on a valid point for woo.
                 # TODO ideally validation would flag this as an error.
                 continue
-            is_abs = (trigger.offset_is_absolute or
-                      trigger.offset_is_from_icp)
-            if is_abs and parent_point != point:
-                # If 'foo[^] => bar' only spawn off of '^'.
-                continue
+            is_abs = trigger.offset_is_absolute or trigger.offset_is_from_icp
             graph_parents[seq].append((parent_name, parent_point, is_abs))
 
     if tdef.sequential:
diff --git a/tests/integration/test_data_store_mgr.py b/tests/integration/test_data_store_mgr.py
index 4d808bacc0a..906b1ac052d 100644
--- a/tests/integration/test_data_store_mgr.py
+++ b/tests/integration/test_data_store_mgr.py
@@ -18,6 +18,7 @@
 from typing import TYPE_CHECKING
 
 from cylc.flow.data_store_mgr import (
+    EDGES,
     FAMILY_PROXIES,
     JOBS,
     TASKS,
@@ -316,3 +317,36 @@ def test_delta_task_prerequisite(harness):
         p.satisfied
         for t in schd.data_store_mgr.updated[TASK_PROXIES].values()
         for p in t.prerequisites})
+
+
+async def test_absolute_graph_edges(flow, scheduler, start):
+    """It should add absolute graph edges to the store.
+
+    See: https://github.com/cylc/cylc-flow/issues/5845
+    """
+    runahead_cycles = 1
+    id_ = flow({
+        'scheduling': {
+            'initial cycle point': '1',
+            'cycling mode': 'integer',
+            'runahead limit': f'P{runahead_cycles}',
+            'graph': {
+                'R1': 'build',
+                'P1': 'build[^] => run',
+            },
+        },
+    })
+    schd = scheduler(id_)
+
+    async with start(schd):
+        await schd.update_data_structure()
+
+        assert {
+            (Tokens(edge.source).relative_id, Tokens(edge.target).relative_id)
+            for edge in schd.data_store_mgr.data[schd.id][EDGES].values()
+        } == {
+            ('1/build', f'{cycle}/run')
+            # +1 for Python's range()
+            # +2 for Cylc's runahead
+            for cycle in range(1, runahead_cycles + 3)
+        }