diff --git a/balm/SuccessionDiagram.py b/balm/SuccessionDiagram.py
index 9f14fe90..e1aadf63 100644
--- a/balm/SuccessionDiagram.py
+++ b/balm/SuccessionDiagram.py
@@ -93,6 +93,14 @@ class SuccessionDiagram:
 
     """
 
+    __slots__ = (
+        "network",
+        "petri_net",
+        "nfvs",
+        "dag",
+        "node_indices",
+    )
+
     def __init__(self, network: BooleanNetwork):
         # Original Boolean network.
         self.network = network
@@ -103,7 +111,7 @@ def __init__(self, network: BooleanNetwork):
             network, parity="negative"
         )  # find_minimum_NFVS(network)
         # A directed acyclic graph representing the succession diagram.
-        self.G = nx.DiGraph()
+        self.dag = nx.DiGraph()
         # A dictionary used for uniqueness checks on the nodes of the succession
         # diagram. See `SuccessionDiagram.ensure_node` for details.
         self.node_indices: dict[int, int] = {}
@@ -116,7 +124,7 @@ def __getstate__(self) -> dict[str, str | nx.DiGraph | list[str] | dict[int, int
             "network rules": self.network.to_aeon(),
             "petri net": self.petri_net,
             "nfvs": self.nfvs,
-            "G": self.G,
+            "G": self.dag,
             "node_indices": self.node_indices,
         }
         return state
@@ -127,14 +135,14 @@ def __setstate__(
         self.network = BooleanNetwork.from_aeon(str(state["network rules"]))
         self.petri_net = cast(nx.DiGraph, state["petri net"])
         self.nfvs = cast(list[str], state["nfvs"])
-        self.G = cast(nx.DiGraph, state["G"])  # type: ignore
+        self.dag = cast(nx.DiGraph, state["G"])  # type: ignore
         self.node_indices = cast(dict[str, int], state["node_indices"])  # type: ignore
 
     def __len__(self) -> int:
         """
         Returns the number of nodes in this `SuccessionDiagram`.
         """
-        return self.G.number_of_nodes()
+        return self.dag.number_of_nodes()
 
     @staticmethod
     def from_aeon(model: str) -> SuccessionDiagram:
@@ -218,7 +226,7 @@ def depth(self) -> int:
         Depth is counted from zero (root has depth zero).
         """
         d = 0
-        for node in cast(set[int], self.G.nodes()):
+        for node in cast(set[int], self.dag.nodes()):
             d = max(d, self.node_depth(int(node)))
         return d
 
@@ -325,7 +333,7 @@ def node_depth(self, node_id: int) -> int:
         Get the depth associated with the provided `node_id`. The depth is counted
         as the longest path from the root node to the given node.
         """
-        return cast(int, self.G.nodes[node_id]["depth"])
+        return cast(int, self.dag.nodes[node_id]["depth"])
 
     def node_space(self, node_id: int) -> dict[str, int]:
         """
@@ -334,21 +342,21 @@ def node_space(self, node_id: int) -> dict[str, int]:
         Note that this is the space *after* percolation. Hence it can hold that
         `|node_space(child)| < |node_space(parent)| + |stable_motif(parent, child)|`.
         """
-        return cast(dict[str, int], self.G.nodes[node_id]["space"])
+        return cast(dict[str, int], self.dag.nodes[node_id]["space"])
 
     def node_is_expanded(self, node_id: int) -> bool:
         """
         True if the successors of the given node are already computed.
         """
-        return cast(bool, self.G.nodes[node_id]["expanded"])
+        return cast(bool, self.dag.nodes[node_id]["expanded"])
 
     def node_is_minimal(self, node_id: int) -> bool:
         """
         True if the node is expanded and it has no successors, i.e. it is a
         minimal trap space.
         """
-        is_leaf: bool = self.G.out_degree(node_id) == 0  # type: ignore
-        return is_leaf and self.G.nodes[node_id]["expanded"]  # type: ignore
+        is_leaf: bool = self.dag.out_degree(node_id) == 0  # type: ignore
+        return is_leaf and self.dag.nodes[node_id]["expanded"]  # type: ignore
 
     def node_successors(self, node_id: int, compute: bool = False) -> list[int]:
         """
@@ -369,13 +377,13 @@ def node_successors(self, node_id: int, compute: bool = False) -> list[int]:
         data but is not expanded, this data will be deleted as it is no longer
         up to date.
         """
-        node = cast(dict[str, Any], self.G.nodes[node_id])
+        node = cast(dict[str, Any], self.dag.nodes[node_id])
         if not node["expanded"] and not compute:
             raise KeyError(f"Node {node_id} is not expanded.")
         if not node["expanded"]:
             self._expand_one_node(node_id)
 
-        return list(self.G.successors(node_id))  # type: ignore
+        return list(self.dag.successors(node_id))  # type: ignore
 
     def node_attractor_seeds(
         self, node_id: int, compute: bool = False
@@ -391,7 +399,7 @@ def node_attractor_seeds(
         same attractor in multiple stub nodes, if the stub nodes intersect), and
         (b) this data is erased if the stub node is expanded later on.
         """
-        node = cast(dict[str, Any], self.G.nodes[node_id])
+        node = cast(dict[str, Any], self.dag.nodes[node_id])
 
         attractors = cast(list[dict[str, int]] | None, node["attractors"])
 
@@ -423,12 +431,12 @@ def edge_stable_motif(
                 dict[str, int],
                 {
                     k: v
-                    for k, v in self.G.edges[parent_id, child_id]["motif"].items()  # type: ignore
+                    for k, v in self.dag.edges[parent_id, child_id]["motif"].items()  # type: ignore
                     if k not in self.node_space(parent_id)
                 },
             )
         else:
-            return cast(dict[str, int], self.G.edges[parent_id, child_id]["motif"])
+            return cast(dict[str, int], self.dag.edges[parent_id, child_id]["motif"])
 
     def build(self):
         """
@@ -549,10 +557,10 @@ def _update_node_depth(self, node_id: int, parent_id: int):
 
         Note that the depth can only increase.
         """
-        assert self.G.edges[parent_id, node_id] is not None
-        parent_depth = cast(int, self.G.nodes[parent_id]["depth"])
-        current_depth = cast(int, self.G.nodes[node_id]["depth"])
-        self.G.nodes[node_id]["depth"] = max(current_depth, parent_depth + 1)
+        assert self.dag.edges[parent_id, node_id] is not None
+        parent_depth = cast(int, self.dag.nodes[parent_id]["depth"])
+        current_depth = cast(int, self.dag.nodes[node_id]["depth"])
+        self.dag.nodes[node_id]["depth"] = max(current_depth, parent_depth + 1)
 
     def _expand_one_node(self, node_id: int):
         """
@@ -566,7 +574,7 @@ def _expand_one_node(self, node_id: int):
         If there are already some attractor data for this node (stub nodes can
         have associated attractor data), this data is erased.
         """
-        node = cast(dict[str, Any], self.G.nodes[node_id])
+        node = cast(dict[str, Any], self.dag.nodes[node_id])
         if node["expanded"]:
             return
 
@@ -631,8 +639,8 @@ def _ensure_node(self, parent_id: int | None, stable_motif: dict[str, int]) -> i
 
         child_id = None
         if key not in self.node_indices:
-            child_id = self.G.number_of_nodes()
-            self.G.add_node(  # type: ignore
+            child_id = self.dag.number_of_nodes()
+            self.dag.add_node(  # type: ignore
                 child_id,
                 id=child_id,  # In case we ever need it within the "node data" dictionary.
                 space=fixed_vars,
@@ -650,7 +658,7 @@ def _ensure_node(self, parent_id: int | None, stable_motif: dict[str, int]) -> i
             # TODO: It seems that there are some networks where the same child
             # can be reached through multiple stable motifs. Not sure how to
             # approach these... but this is probably good enough for now.
-            self.G.add_edge(parent_id, child_id, motif=stable_motif)  # type: ignore
+            self.dag.add_edge(parent_id, child_id, motif=stable_motif)  # type: ignore
             self._update_node_depth(child_id, parent_id)
 
         return child_id
diff --git a/balm/_sd_algorithms/expand_source_SCCs.py b/balm/_sd_algorithms/expand_source_SCCs.py
index 648b7a6c..dc271e81 100644
--- a/balm/_sd_algorithms/expand_source_SCCs.py
+++ b/balm/_sd_algorithms/expand_source_SCCs.py
@@ -61,7 +61,7 @@ def expand_source_SCCs(
 
     # percolate constant nodes
     perc_space = percolate_space(sd.network, {}, strict_percolation=False)
-    sd.G.nodes[root]["space"] = perc_space
+    sd.dag.nodes[root]["space"] = perc_space
 
     # find source nodes
     perc_bn = percolate_network(sd.network, perc_space)
@@ -78,8 +78,8 @@ def expand_source_SCCs(
 
             next_level.append(sd._ensure_node(root, sub_space))  # type: ignore
 
-        sd.G.nodes[root]["expanded"] = True
-        sd.G.nodes[root]["attractors"] = []  # no need to look for attractors here
+        sd.dag.nodes[root]["expanded"] = True
+        sd.dag.nodes[root]["attractors"] = []  # no need to look for attractors here
         current_level = next_level
         next_level = []
 
@@ -89,7 +89,7 @@ def expand_source_SCCs(
 
         # each level consists of one round of fixing all source SCCs
         for node_id in current_level:
-            sub_space = cast(dict[str, int], sd.G.nodes[node_id]["space"])
+            sub_space = cast(dict[str, int], sd.dag.nodes[node_id]["space"])
 
             # find source SCCs
             clean_bnet, clean_bn = perc_and_remove_constants_from_bn(perc_bn, sub_space)
@@ -141,8 +141,8 @@ def expand_source_SCCs(
         print(f"{final_level=}")
     for node_id in final_level:
         # These assertions should be unnecessary, but just to be sure.
-        assert not sd.G.nodes[node_id]["expanded"]  # expand nodes from here
-        assert sd.G.nodes[node_id]["attractors"] is None  # check attractors from here
+        assert not sd.dag.nodes[node_id]["expanded"]  # expand nodes from here
+        assert sd.dag.nodes[node_id]["attractors"] is None  # check attractors from here
 
         # restore this once we allow all expansion algorithms to expand from a node
         # expander(sd, node_id)
@@ -317,11 +317,11 @@ def find_scc_sd(
     # delete the implicit parameters from the node subspaces and the edge motifs
     for node_id in scc_sd.node_ids():
         for implicit in implicit_parameters:
-            cast(dict[str, int], scc_sd.G.nodes[node_id]["space"]).pop(implicit, None)
+            cast(dict[str, int], scc_sd.dag.nodes[node_id]["space"]).pop(implicit, None)
 
-    for x, y in cast(Iterable[tuple[int, int]], scc_sd.G.edges):
+    for x, y in cast(Iterable[tuple[int, int]], scc_sd.dag.edges):
         for implicit in implicit_parameters:
-            cast(dict[str, int], scc_sd.G.edges[x, y]["motif"]).pop(implicit, None)
+            cast(dict[str, int], scc_sd.dag.edges[x, y]["motif"]).pop(implicit, None)
 
     return scc_sd, exist_maa
 
@@ -346,14 +346,14 @@ def attach_scc_sd(
         return [branch]
 
     next_branches: list[int] = []
-    size_before_attach = sd.G.number_of_nodes()
+    size_before_attach = sd.dag.number_of_nodes()
     # first add all the nodes using their first parent
     for scc_node_id in scc_sd.node_ids():
         if scc_node_id == 0:  # no need to add the root of scc_sd
             continue
 
         scc_parent_id = cast(
-            int, list(scc_sd.G.predecessors(scc_node_id))[0]  # type: ignore
+            int, list(scc_sd.dag.predecessors(scc_node_id))[0]  # type: ignore
         )  # get the first parent
         assert scc_parent_id < scc_node_id
 
@@ -363,11 +363,11 @@ def attach_scc_sd(
             parent_id = size_before_attach + scc_parent_id - 1
 
         motif = scc_sd.edge_stable_motif(scc_parent_id, scc_node_id)
-        motif.update(cast(dict[str, int], sd.G.nodes[branch]["space"]))
+        motif.update(cast(dict[str, int], sd.dag.nodes[branch]["space"]))
 
         child_id = sd._ensure_node(parent_id, motif)  # type: ignore
         if check_maa:
-            sd.G.nodes[parent_id][
+            sd.dag.nodes[parent_id][
                 "attractors"
             ] = []  # no need to check for attractors in these nodes
 
@@ -381,16 +381,16 @@ def attach_scc_sd(
         else:
             parent_id = size_before_attach + scc_node_id - 1
 
-        scc_child_ids = cast(list[int], list(scc_sd.G.successors(scc_node_id)))  # type: ignore
+        scc_child_ids = cast(list[int], list(scc_sd.dag.successors(scc_node_id)))  # type: ignore
         for scc_child_id in scc_child_ids:
             motif = scc_sd.edge_stable_motif(scc_node_id, scc_child_id)
-            motif.update(cast(dict[str, int], sd.G.nodes[branch]["space"]))
+            motif.update(cast(dict[str, int], sd.dag.nodes[branch]["space"]))
 
             child_id = sd._ensure_node(parent_id, motif)  # type: ignore
             assert child_id == size_before_attach + scc_child_id - 1
 
         # if the node had any child node, consider it expanded.
         if len(scc_child_ids) > 0:
-            sd.G.nodes[parent_id]["expanded"] = True
+            sd.dag.nodes[parent_id]["expanded"] = True
 
     return next_branches
diff --git a/balm/control.py b/balm/control.py
index 454182bd..6bd0f499 100644
--- a/balm/control.py
+++ b/balm/control.py
@@ -212,7 +212,7 @@ def successions_to_target(
         for path in cast(
             list[list[int]],
             nx.all_simple_paths(  # type: ignore
-                succession_diagram.G,
+                succession_diagram.dag,
                 source=succession_diagram.root(),
                 target=s,
             ),
diff --git a/tests/source_SCC_test.py b/tests/source_SCC_test.py
index 980eb9de..b1080413 100644
--- a/tests/source_SCC_test.py
+++ b/tests/source_SCC_test.py
@@ -1,5 +1,6 @@
 from biodivine_aeon import BooleanNetwork
 
+import balm.SuccessionDiagram
 from balm._sd_algorithms.expand_source_SCCs import (
     expand_source_SCCs,
     find_scc_sd,
@@ -7,7 +8,6 @@
     perc_and_remove_constants_from_bn,
 )
 from balm.space_utils import percolate_network, percolate_space
-from balm.SuccessionDiagram import SuccessionDiagram
 
 
 def test_find_source_nodes():
@@ -68,16 +68,19 @@ def test_find_scc_sd():
 B, A | A &  C"""
 
     scc_sd, _ = find_scc_sd(
-        bnet, ["A", "B"], expander=SuccessionDiagram.expand_bfs, check_maa=True
+        bnet,
+        ["A", "B"],
+        expander=balm.SuccessionDiagram.SuccessionDiagram.expand_bfs,
+        check_maa=True,
     )
 
-    assert scc_sd.G.nodes[0]["space"] == {}
-    assert scc_sd.G.nodes[1]["space"] == {"A": 0, "B": 0}
-    assert scc_sd.G.nodes[2]["space"] == {"A": 1, "B": 1}
+    assert scc_sd.dag.nodes[0]["space"] == {}
+    assert scc_sd.dag.nodes[1]["space"] == {"A": 0, "B": 0}
+    assert scc_sd.dag.nodes[2]["space"] == {"A": 1, "B": 1}
 
 
 def expansion(bn: BooleanNetwork):
-    sd = SuccessionDiagram(bn)
+    sd = balm.SuccessionDiagram.SuccessionDiagram(bn)
     fully_expanded = expand_source_SCCs(sd, check_maa=False)
     assert fully_expanded
 
@@ -134,7 +137,7 @@ def test_expansion():
 
 
 def attractor_search(bn: BooleanNetwork):
-    sd = SuccessionDiagram(bn)
+    sd = balm.SuccessionDiagram.SuccessionDiagram(bn)
     fully_expanded = expand_source_SCCs(sd)
     assert fully_expanded
 
@@ -358,10 +361,10 @@ def test_isomorph():
     path = "models/bbm-bnet-inputs-true/005.bnet"
     bn = BooleanNetwork.from_file(path)
 
-    sd_bfs = SuccessionDiagram(bn)
+    sd_bfs = balm.SuccessionDiagram.SuccessionDiagram(bn)
     sd_bfs.expand_bfs()
 
-    sd_scc = SuccessionDiagram(bn)
+    sd_scc = balm.SuccessionDiagram.SuccessionDiagram(bn)
     expand_source_SCCs(sd_scc)
 
     assert [sd_bfs.node_space(id) for id in sd_bfs.node_ids()] == [
@@ -370,7 +373,7 @@ def test_isomorph():
 
     assert sd_scc.is_isomorphic(sd_bfs)
 
-    edge_motifs_bfs = set(str(sorted(sd_bfs.edge_stable_motif(x, y).items())) for (x, y) in sd_bfs.G.edges)  # type: ignore
-    edge_motifs_scc = set(str(sorted(sd_scc.edge_stable_motif(x, y).items())) for (x, y) in sd_scc.G.edges)  # type: ignore
+    edge_motifs_bfs = set(str(sorted(sd_bfs.edge_stable_motif(x, y).items())) for (x, y) in sd_bfs.dag.edges)  # type: ignore
+    edge_motifs_scc = set(str(sorted(sd_scc.edge_stable_motif(x, y).items())) for (x, y) in sd_scc.dag.edges)  # type: ignore
 
     assert edge_motifs_bfs == edge_motifs_scc
diff --git a/tests/succession_diagram_test.py b/tests/succession_diagram_test.py
index 634996ee..aeb0da9d 100644
--- a/tests/succession_diagram_test.py
+++ b/tests/succession_diagram_test.py
@@ -24,9 +24,9 @@ def test_succession_diagram_structure(self):
 
         succession_diagram = SuccessionDiagram(bn)
         succession_diagram.expand_bfs()
-        assert succession_diagram.G.number_of_nodes() == 3
-        assert succession_diagram.G.number_of_edges() == 2  # type: ignore
-        assert max(d["depth"] for _, d in succession_diagram.G.nodes(data=True)) == 1  # type: ignore
+        assert succession_diagram.dag.number_of_nodes() == 3
+        assert succession_diagram.dag.number_of_edges() == 2  # type: ignore
+        assert max(d["depth"] for _, d in succession_diagram.dag.nodes(data=True)) == 1  # type: ignore
         assert succession_diagram.depth() == 1
         assert (
             max(
@@ -74,9 +74,9 @@ def test_succession_diagram_structure(self):
 
         # Then expand the whole thing.
         succession_diagram.expand_bfs()
-        assert succession_diagram.G.number_of_nodes() == 4
-        assert succession_diagram.G.number_of_edges() == 5  # type: ignore
-        assert max(d["depth"] for _, d in succession_diagram.G.nodes(data=True)) == 2  # type: ignore
+        assert succession_diagram.dag.number_of_nodes() == 4
+        assert succession_diagram.dag.number_of_edges() == 5  # type: ignore
+        assert max(d["depth"] for _, d in succession_diagram.dag.nodes(data=True)) == 2  # type: ignore
         assert succession_diagram.depth() == 2
         assert (
             max(