diff --git a/src/poetry/puzzle/solver.py b/src/poetry/puzzle/solver.py
index 32bd327a7be..1fe47fe4350 100644
--- a/src/poetry/puzzle/solver.py
+++ b/src/poetry/puzzle/solver.py
@@ -1,6 +1,5 @@
 from __future__ import annotations
 
-import enum
 import time
 
 from collections import defaultdict
@@ -140,11 +139,9 @@ def _solve(self, use_latest: list[str] = None) -> tuple[list[Package], list[int]
         except SolveFailure as e:
             raise SolverProblemError(e)
 
-        # NOTE passing explicit empty array for seen to reset between invocations during
-        # update + install cycle
         results = dict(
             depth_first_search(
-                PackageNode(self._package, packages, seen=[]), aggregate_package_nodes
+                PackageNode(self._package, packages), aggregate_package_nodes
             )
         )
 
@@ -194,27 +191,19 @@ def __str__(self) -> str:
         return str(self.id)
 
 
-class VisitedState(enum.Enum):
-    Unvisited = 0
-    PartiallyVisited = 1
-    Visited = 2
-
-
 def depth_first_search(
     source: PackageNode, aggregator: Callable
 ) -> list[tuple[Package, int]]:
     back_edges: dict[DFSNodeID, list[PackageNode]] = defaultdict(list)
-    visited: dict[DFSNodeID, VisitedState] = {}
+    visited: set[DFSNodeID] = set()
     topo_sorted_nodes: list[PackageNode] = []
 
     dfs_visit(source, back_edges, visited, topo_sorted_nodes)
 
     # Combine the nodes by name
     combined_nodes = defaultdict(list)
-    name_children = defaultdict(list)
     for node in topo_sorted_nodes:
         node.visit(back_edges[node.id])
-        name_children[node.name].extend(node.reachable())
         combined_nodes[node.name].append(node)
 
     combined_topo_sorted_nodes = [
@@ -223,34 +212,23 @@ def depth_first_search(
         if node.name in combined_nodes
     ]
 
-    return [
-        aggregator(nodes, name_children[nodes[0].name])
-        for nodes in combined_topo_sorted_nodes
-    ]
+    return [aggregator(nodes) for nodes in combined_topo_sorted_nodes]
 
 
 def dfs_visit(
     node: PackageNode,
     back_edges: dict[DFSNodeID, list[PackageNode]],
-    visited: dict[DFSNodeID, VisitedState],
+    visited: set[DFSNodeID],
     sorted_nodes: list[PackageNode],
-) -> bool:
-    if visited.get(node.id, VisitedState.Unvisited) == VisitedState.Visited:
-        return True
-    if visited.get(node.id, VisitedState.Unvisited) == VisitedState.PartiallyVisited:
-        # We have a circular dependency.
-        # Since the dependencies are resolved we can
-        # simply skip it because we already have it
-        return True
-
-    visited[node.id] = VisitedState.PartiallyVisited
+) -> None:
+    if node.id in visited:
+        return
+    visited.add(node.id)
+
     for neighbor in node.reachable():
         back_edges[neighbor.id].append(node)
-        if not dfs_visit(neighbor, back_edges, visited, sorted_nodes):
-            return False
-    visited[node.id] = VisitedState.Visited
+        dfs_visit(neighbor, back_edges, visited, sorted_nodes)
     sorted_nodes.insert(0, node)
-    return True
 
 
 class PackageNode(DFSNode):
@@ -258,7 +236,6 @@ def __init__(
         self,
         package: Package,
         packages: list[Package],
-        seen: list[Package],
         previous: PackageNode | None = None,
         previous_dep: None
         | (
@@ -279,7 +256,6 @@ def __init__(
     ) -> None:
         self.package = package
         self.packages = packages
-        self.seen = seen
 
         self.previous = previous
         self.previous_dep = previous_dep
@@ -306,12 +282,6 @@ def __init__(
     def reachable(self) -> list[PackageNode]:
         children: list[PackageNode] = []
 
-        # skip already traversed packages
-        if self.package in self.seen:
-            return []
-        else:
-            self.seen.append(self.package)
-
         if (
             self.dep
             and self.previous_dep
@@ -348,7 +318,6 @@ def reachable(self) -> list[PackageNode]:
                         PackageNode(
                             pkg,
                             self.packages,
-                            self.seen,
                             self,
                             dependency,
                             self.dep or dependency,
@@ -369,19 +338,15 @@ def visit(self, parents: list[PackageNode]) -> None:
         )
 
 
-def aggregate_package_nodes(
-    nodes: list[PackageNode], children: list[PackageNode]
-) -> tuple[Package, int]:
+def aggregate_package_nodes(nodes: list[PackageNode]) -> tuple[Package, int]:
     package = nodes[0].package
     depth = max(node.depth for node in nodes)
     groups: list[str] = []
     for node in nodes:
         groups.extend(node.groups)
 
-    category = (
-        "main" if any("default" in node.groups for node in children + nodes) else "dev"
-    )
-    optional = all(node.optional for node in children + nodes)
+    category = "main" if any("default" in node.groups for node in nodes) else "dev"
+    optional = all(node.optional for node in nodes)
     for node in nodes:
         node.depth = depth
         node.category = category