diff --git a/stable_baselines3/common/buffers.py b/stable_baselines3/common/buffers.py
index fe633e1af..75d506183 100644
--- a/stable_baselines3/common/buffers.py
+++ b/stable_baselines3/common/buffers.py
@@ -6,14 +6,18 @@
 import torch as th
 from gymnasium import spaces
 
+from torch_geometric.data import Data, Batch
+
 from stable_baselines3.common.preprocessing import get_action_dim, get_obs_shape
 from stable_baselines3.common.type_aliases import (
     DictReplayBufferSamples,
     DictRolloutBufferSamples,
     ReplayBufferSamples,
     RolloutBufferSamples,
+    GraphRolloutBufferSamples,
 )
 from stable_baselines3.common.utils import get_device
+from stable_baselines3.common.vec_env.util import dict_to_obs, graph_copy_obs_dict
 from stable_baselines3.common.vec_env import VecNormalize
 
 try:
@@ -439,7 +443,6 @@ def add(
 
         # Reshape to handle multi-dim and discrete action spaces, see GH #970 #1392
         action = action.reshape((self.n_envs, self.action_dim))
-
         self.observations[self.pos] = np.array(obs).copy()
         self.actions[self.pos] = np.array(action).copy()
         self.rewards[self.pos] = np.array(reward).copy()
@@ -493,6 +496,214 @@ def _get_samples(
         return RolloutBufferSamples(*tuple(map(self.to_torch, data)))
 
 
+class GraphRolloutBuffer(BaseBuffer):
+    """
+    Rollout buffer used in on-policy algorithms like A2C/PPO.
+    It corresponds to ``buffer_size`` transitions collected
+    using the current policy.
+    This experience will be discarded after the policy update.
+    In order to use PPO objective, we also store the current value of each state
+    and the log probability of each taken action.
+
+    The term rollout here refers to the model-free notion and should not
+    be used with the concept of rollout used in model-based RL or planning.
+    Hence, it is only involved in policy and value function training but not action selection.
+
+    :param buffer_size: Max number of element in the buffer
+    :param observation_space: Observation space
+    :param action_space: Action space
+    :param device: PyTorch device
+    :param gae_lambda: Factor for trade-off of bias vs variance for Generalized Advantage Estimator
+        Equivalent to classic advantage when set to 1.
+    :param gamma: Discount factor
+    :param n_envs: Number of parallel environments
+    """
+
+    observations: np.ndarray
+    actions: np.ndarray
+    rewards: np.ndarray
+    advantages: np.ndarray
+    returns: np.ndarray
+    episode_starts: np.ndarray
+    log_probs: np.ndarray
+    values: np.ndarray
+
+    def __init__(
+        self,
+        buffer_size: int,
+        observation_space: spaces.Space,
+        action_space: spaces.Space,
+        device: Union[th.device, str] = "auto",
+        gae_lambda: float = 1,
+        gamma: float = 0.99,
+        n_envs: int = 1,
+    ):
+        super().__init__(buffer_size, observation_space, action_space, device, n_envs=n_envs)
+        assert isinstance(self.observation_space, spaces.Graph), "Graph buffer"
+
+        self.gae_lambda = gae_lambda
+        self.gamma = gamma
+        self.generator_ready = False
+        self.observations = {"node": {}, "edge_weight": {}, "edge_index": {}}
+        self.reset()
+
+    def reset(self) -> None:
+        self.observations = {"node": {}, "edge_weight": {}, "edge_index": {}}  # variable size
+        self.actions = {}
+        self.rewards = np.zeros((self.buffer_size, self.n_envs), dtype=np.float32)
+        self.returns = np.zeros((self.buffer_size, self.n_envs), dtype=np.float32)
+        self.episode_starts = np.zeros((self.buffer_size, self.n_envs), dtype=np.float32)
+        self.values = np.zeros((self.buffer_size, self.n_envs), dtype=np.float32)
+        self.log_probs = {}
+        self.advantages = np.zeros((self.buffer_size, self.n_envs), dtype=np.float32)
+        self.generator_ready = False
+        super().reset()
+
+    def compute_returns_and_advantage(self, last_values: th.Tensor, dones: np.ndarray) -> None:
+        """
+        Post-processing step: compute the lambda-return (TD(lambda) estimate)
+        and GAE(lambda) advantage.
+
+        Uses Generalized Advantage Estimation (https://arxiv.org/abs/1506.02438)
+        to compute the advantage. To obtain Monte-Carlo advantage estimate (A(s) = R - V(S))
+        where R is the sum of discounted reward with value bootstrap
+        (because we don't always have full episode), set ``gae_lambda=1.0`` during initialization.
+
+        The TD(lambda) estimator has also two special cases:
+        - TD(1) is Monte-Carlo estimate (sum of discounted rewards)
+        - TD(0) is one-step estimate with bootstrapping (r_t + gamma * v(s_{t+1}))
+
+        For more information, see discussion in https://github.com/DLR-RM/stable-baselines3/pull/375.
+
+        :param last_values: state value estimation for the last step (one for each env)
+        :param dones: if the last step was a terminal step (one bool for each env).
+        """
+        # Convert to numpy
+        last_values = last_values.clone().cpu().numpy().flatten()
+
+        last_gae_lam = 0
+        for step in reversed(range(self.buffer_size)):
+            if step == self.buffer_size - 1:
+                next_non_terminal = 1.0 - dones
+                next_values = last_values
+            else:
+                next_non_terminal = 1.0 - self.episode_starts[step + 1]
+                next_values = self.values[step + 1]
+            delta = self.rewards[step] + self.gamma * next_values * next_non_terminal - self.values[step]
+            last_gae_lam = delta + self.gamma * self.gae_lambda * next_non_terminal * last_gae_lam
+            self.advantages[step] = last_gae_lam
+        # TD(lambda) estimator, see Github PR #375 or "Telescoping in TD(lambda)"
+        # in David Silver Lecture 4: https://www.youtube.com/watch?v=PnHCvfgC_ZA
+        self.returns = self.advantages + self.values
+
+    def add(
+        self,
+        obs: np.ndarray,
+        action: np.ndarray,
+        reward: np.ndarray,
+        episode_start: np.ndarray,
+        value: th.Tensor,
+        log_prob: th.Tensor,
+    ) -> None:
+        """
+        :param obs: Observation
+        :param action: Action -- assumed to be ndarray by clipping
+        :param reward:
+        :param episode_start: Start of episode signal.
+        :param value: estimated value of the current state
+            following the current policy.
+        :param log_prob: log probability of the action
+            following the current policy.
+        """
+        if isinstance(log_prob, List):
+            if len(log_prob) == 1:
+                log_prob = log_prob[0].cpu()
+            else:
+                raise NotImplementedError
+        if len(log_prob.shape) == 0:
+            # Reshape 0-d tensor to avoid error
+            log_prob = log_prob.reshape(-1, 1)
+
+        # Reshape needed when using multiple envs with discrete observations
+        # as numpy cannot broadcast (n_discrete,) to (n_discrete, 1)
+        if isinstance(self.observation_space, spaces.Discrete):
+            obs = obs.reshape((self.n_envs, *self.obs_shape))
+
+        # Reshape to handle multi-dim and discrete action spaces, see GH #970 #1392
+        if isinstance(action, List):
+            if len(action) == 1:
+                action = action[0]
+            else:
+                # Probably loop trough and add each entry independently into the buffer
+                raise NotImplementedError
+        else:
+            action = action.reshape((self.n_envs, self.action_dim))
+
+        assert isinstance(obs, Data)
+        self.observations["node"][self.pos] = obs.x  # should be a pyg Data entry
+        self.observations["edge_index"][self.pos] = obs.edge_index
+        self.observations["edge_weight"][self.pos] = obs.w
+
+        self.actions[self.pos] = np.array(action).copy()
+        self.rewards[self.pos] = np.array(reward).copy()
+        self.episode_starts[self.pos] = np.array(episode_start).copy()
+        self.values[self.pos] = value.clone().cpu().numpy().flatten()
+        self.log_probs[self.pos] = log_prob.clone().cpu().numpy()
+        self.pos += 1
+        if self.pos == self.buffer_size:
+            self.full = True
+
+    def get(self, batch_size: Optional[int] = None) -> Generator[RolloutBufferSamples, None, None]:
+        assert self.full, ""
+        indices = np.random.permutation(self.buffer_size * self.n_envs)
+        # Prepare the data
+
+        if not self.generator_ready:
+            self.observations = dict_to_obs(self.observation_space, self.observations)
+            assert all([isinstance(k, int) for k in self.actions.keys()]), f"Action not indexed correctly"
+            self.actions_flat = np.stack([self.actions[i] for i in range(len(self.actions.keys()))])
+            self.actions = self.actions_flat
+
+            assert all([isinstance(k, int) for k in self.log_probs.keys()]), f"Action not indexed correctly"
+            self.log_probs_flat = np.stack([self.log_probs[i] for i in range(len(self.log_probs.keys()))])
+            self.log_probs = self.log_probs_flat
+
+            _tensor_names = [
+                "values",
+                "advantages",
+                "returns",
+            ]
+
+            for tensor in _tensor_names:
+                self.__dict__[tensor] = self.swap_and_flatten(self.__dict__[tensor])
+            self.generator_ready = True
+
+        # Return everything, don't create minibatches
+        if batch_size is None:
+            batch_size = self.buffer_size * self.n_envs
+
+        start_idx = 0
+        while start_idx < self.buffer_size * self.n_envs:
+            yield self._get_samples(indices[start_idx : start_idx + batch_size])
+            start_idx += batch_size
+
+    def _get_samples(
+        self,
+        batch_inds: np.ndarray,
+        env: Optional[VecNormalize] = None,
+    ) -> RolloutBufferSamples:  # type: ignore[signature-mismatch] #FIXME
+        data = (
+            Batch.from_data_list(self.observations[batch_inds]),
+            self.to_torch(self.actions[batch_inds]),
+            self.to_torch(self.values[batch_inds].flatten()),
+            self.to_torch(self.log_probs[batch_inds]),
+            self.to_torch(self.advantages[batch_inds]),
+            self.to_torch(self.returns[batch_inds].flatten()),
+        )
+
+        return GraphRolloutBufferSamples(*tuple(data))
+
+
 class DictReplayBuffer(ReplayBuffer):
     """
     Dict Replay buffer used in off-policy algorithms like SAC/TD3.
@@ -681,8 +892,6 @@ class DictRolloutBuffer(RolloutBuffer):
     :param n_envs: Number of parallel environments
     """
 
-    observations: Dict[str, np.ndarray]
-
     def __init__(
         self,
         buffer_size: int,
@@ -699,7 +908,8 @@ def __init__(
 
         self.gae_lambda = gae_lambda
         self.gamma = gamma
-
+        self.observations, self.actions, self.rewards, self.advantages = None, None, None, None
+        self.returns, self.episode_starts, self.values, self.log_probs = None, None, None, None
         self.generator_ready = False
         self.reset()
 
diff --git a/stable_baselines3/common/on_policy_algorithm.py b/stable_baselines3/common/on_policy_algorithm.py
index 87e192990..76e2e4bba 100644
--- a/stable_baselines3/common/on_policy_algorithm.py
+++ b/stable_baselines3/common/on_policy_algorithm.py
@@ -7,7 +7,7 @@
 from gymnasium import spaces
 
 from stable_baselines3.common.base_class import BaseAlgorithm
-from stable_baselines3.common.buffers import DictRolloutBuffer, RolloutBuffer
+from stable_baselines3.common.buffers import DictRolloutBuffer, RolloutBuffer, GraphRolloutBuffer
 from stable_baselines3.common.callbacks import BaseCallback
 from stable_baselines3.common.policies import ActorCriticPolicy
 from stable_baselines3.common.type_aliases import GymEnv, MaybeCallback, Schedule
@@ -100,6 +100,7 @@ def __init__(
         self.ent_coef = ent_coef
         self.vf_coef = vf_coef
         self.max_grad_norm = max_grad_norm
+        self.episodes = 0
 
         if _init_setup_model:
             self._setup_model()
@@ -107,8 +108,12 @@ def __init__(
     def _setup_model(self) -> None:
         self._setup_lr_schedule()
         self.set_random_seed(self.seed)
-
-        buffer_cls = DictRolloutBuffer if isinstance(self.observation_space, spaces.Dict) else RolloutBuffer
+        if isinstance(self.observation_space, spaces.Dict):
+            buffer_cls = DictRolloutBuffer
+        elif isinstance(self.observation_space, spaces.Graph):
+            buffer_cls = GraphRolloutBuffer
+        else:
+            buffer_cls = RolloutBuffer
 
         self.rollout_buffer = buffer_cls(
             self.n_steps,
@@ -158,6 +163,8 @@ def collect_rollouts(
 
         callback.on_rollout_start()
 
+        self.episodes = 0
+
         while n_steps < n_rollout_steps:
             if self.use_sde and self.sde_sample_freq > 0 and n_steps % self.sde_sample_freq == 0:
                 # Sample a new noise matrix
@@ -167,13 +174,32 @@ def collect_rollouts(
                 # Convert to pytorch tensor or to TensorDict
                 obs_tensor = obs_as_tensor(self._last_obs, self.device)
                 actions, values, log_probs = self.policy(obs_tensor)
-            actions = actions.cpu().numpy()
+                actions, log_probs = actions, log_probs
 
             # Rescale and perform action
             clipped_actions = actions
             # Clip the actions to avoid out of bound error
             if isinstance(self.action_space, spaces.Box):
-                clipped_actions = np.clip(actions, self.action_space.low, self.action_space.high)
+                if isinstance(actions, List):
+                    clipped_actions = [
+                        th.clamp(
+                            a,
+                            min=th.Tensor(self.action_space.low).to(a.device),
+                            max=th.Tensor(self.action_space.high).to(a.device),
+                        )
+                        for a in actions
+                    ]
+                    actions = [a.cpu().numpy() for a in actions]
+                else:
+                    clipped_actions = th.clamp(
+                        actions,
+                        min=th.Tensor(self.action_space.low).to(actions.device),
+                        max=th.Tensor(self.action_space.high).to(actions.device),
+                    )
+                    actions = actions.cpu().numpy()
+            else:
+                clipped_actions = actions.cpu().numpy()
+                actions = actions.cpu().numpy()
 
             new_obs, rewards, dones, infos = env.step(clipped_actions)
 
@@ -203,6 +229,8 @@ def collect_rollouts(
                     with th.no_grad():
                         terminal_value = self.policy.predict_values(terminal_obs)[0]  # type: ignore[arg-type]
                     rewards[idx] += self.gamma * terminal_value
+                if done:
+                    self.episodes += 1
 
             rollout_buffer.add(
                 self._last_obs,  # type: ignore[arg-type]
@@ -273,6 +301,17 @@ def learn(
                 if len(self.ep_info_buffer) > 0 and len(self.ep_info_buffer[0]) > 0:
                     self.logger.record("rollout/ep_rew_mean", safe_mean([ep_info["r"] for ep_info in self.ep_info_buffer]))
                     self.logger.record("rollout/ep_len_mean", safe_mean([ep_info["l"] for ep_info in self.ep_info_buffer]))
+
+                    diff = self.episodes
+                    self.logger.record("result/success", sum([ep_info["success"] for ep_info in self.ep_info_buffer][-diff:]))
+                    self.logger.record("result/failed", sum([ep_info["failed"] for ep_info in self.ep_info_buffer][-diff:]))
+                    self.logger.record(
+                        "result/truncated", sum([ep_info["truncated"] for ep_info in self.ep_info_buffer][-diff:])
+                    )
+                    self.logger.record(
+                        "result/terminated", sum([ep_info["terminated"] for ep_info in self.ep_info_buffer][-diff:])
+                    )
+
                 self.logger.record("time/fps", fps)
                 self.logger.record("time/time_elapsed", int(time_elapsed), exclude="tensorboard")
                 self.logger.record("time/total_timesteps", self.num_timesteps, exclude="tensorboard")
diff --git a/stable_baselines3/common/policies.py b/stable_baselines3/common/policies.py
index 21d2034d6..531c718aa 100644
--- a/stable_baselines3/common/policies.py
+++ b/stable_baselines3/common/policies.py
@@ -624,9 +624,13 @@ def forward(self, obs: th.Tensor, deterministic: bool = False) -> Tuple[th.Tenso
         # Evaluate the values for the given observations
         values = self.value_net(latent_vf)
         distribution = self._get_action_dist_from_latent(latent_pi)
-        actions = distribution.get_actions(deterministic=deterministic)
-        log_prob = distribution.log_prob(actions)
-        actions = actions.reshape((-1, *self.action_space.shape))
+        if isinstance(distribution, List):
+            actions = [d.get_actions(deterministic=deterministic) for d in distribution]
+            log_prob = [d.log_prob(a) for d, a in zip(distribution, actions)]
+        else:
+            actions = distribution.get_actions(deterministic=deterministic)
+            log_prob = distribution.log_prob(actions)
+            actions = actions.reshape((-1, *self.action_space.shape))
         return actions, values, log_prob
 
     def extract_features(self, obs: th.Tensor) -> Union[th.Tensor, Tuple[th.Tensor, th.Tensor]]:
@@ -650,23 +654,36 @@ def _get_action_dist_from_latent(self, latent_pi: th.Tensor) -> Distribution:
         :param latent_pi: Latent code for the actor
         :return: Action distribution
         """
-        mean_actions = self.action_net(latent_pi)
-
-        if isinstance(self.action_dist, DiagGaussianDistribution):
-            return self.action_dist.proba_distribution(mean_actions, self.log_std)
-        elif isinstance(self.action_dist, CategoricalDistribution):
-            # Here mean_actions are the logits before the softmax
-            return self.action_dist.proba_distribution(action_logits=mean_actions)
-        elif isinstance(self.action_dist, MultiCategoricalDistribution):
-            # Here mean_actions are the flattened logits
-            return self.action_dist.proba_distribution(action_logits=mean_actions)
-        elif isinstance(self.action_dist, BernoulliDistribution):
-            # Here mean_actions are the logits (before rounding to get the binary actions)
-            return self.action_dist.proba_distribution(action_logits=mean_actions)
-        elif isinstance(self.action_dist, StateDependentNoiseDistribution):
-            return self.action_dist.proba_distribution(mean_actions, self.log_std, latent_pi)
+        if isinstance(latent_pi, List):  # indicates we're doing one policy to rule them all
+            mean_actions_graphs = [self.action_net(a_latent_pi) for a_latent_pi in latent_pi]
+            if isinstance(self.action_dist, DiagGaussianDistribution):
+                dist = [
+                    self.action_dist.proba_distribution(mean_actions, self.log_std) for mean_actions in mean_actions_graphs
+                ]
+            else:
+                raise NotImplementedError
+            return dist
         else:
-            raise ValueError("Invalid action distribution")
+            mean_actions = self.action_net(latent_pi)
+
+            dist = None
+            if isinstance(self.action_dist, DiagGaussianDistribution):
+                dist = self.action_dist.proba_distribution(mean_actions, self.log_std)
+            elif isinstance(self.action_dist, CategoricalDistribution):
+                # Here mean_actions are the logits before the softmax
+                dist = self.action_dist.proba_distribution(action_logits=mean_actions)
+            elif isinstance(self.action_dist, MultiCategoricalDistribution):
+                # Here mean_actions are the flattened logits
+                dist = self.action_dist.proba_distribution(action_logits=mean_actions)
+            elif isinstance(self.action_dist, BernoulliDistribution):
+                # Here mean_actions are the logits (before rounding to get the binary actions)
+                dist = self.action_dist.proba_distribution(action_logits=mean_actions)
+            elif isinstance(self.action_dist, StateDependentNoiseDistribution):
+                dist = self.action_dist.proba_distribution(mean_actions, self.log_std, latent_pi)
+            else:
+                raise ValueError("Invalid action distribution")
+
+            return dist
 
     def _predict(self, observation: th.Tensor, deterministic: bool = False) -> th.Tensor:
         """
@@ -697,9 +714,17 @@ def evaluate_actions(self, obs: th.Tensor, actions: th.Tensor) -> Tuple[th.Tenso
             latent_pi = self.mlp_extractor.forward_actor(pi_features)
             latent_vf = self.mlp_extractor.forward_critic(vf_features)
         distribution = self._get_action_dist_from_latent(latent_pi)
-        log_prob = distribution.log_prob(actions)
+        if isinstance(distribution, List):
+            log_prob = [d.log_prob(a) for d, a in zip(distribution, actions)]
+            log_prob = th.stack(log_prob)
+            entropy = [d.entropy() for d in distribution]
+            entropy = th.stack(entropy)
+        else:
+            log_prob = distribution.log_prob(actions)
+
+            entropy = distribution.entropy()
         values = self.value_net(latent_vf)
-        entropy = distribution.entropy()
+
         return values, log_prob, entropy
 
     def get_distribution(self, obs: th.Tensor) -> Distribution:
diff --git a/stable_baselines3/common/preprocessing.py b/stable_baselines3/common/preprocessing.py
index bc0959480..6031b6e07 100644
--- a/stable_baselines3/common/preprocessing.py
+++ b/stable_baselines3/common/preprocessing.py
@@ -134,7 +134,8 @@ def preprocess_obs(
         for key, _obs in obs.items():
             preprocessed_obs[key] = preprocess_obs(_obs, observation_space[key], normalize_images=normalize_images)
         return preprocessed_obs
-
+    elif isinstance(observation_space, spaces.Graph):
+        return obs
     else:
         raise NotImplementedError(f"Preprocessing not implemented for {observation_space}")
 
@@ -161,7 +162,8 @@ def get_obs_shape(
         return observation_space.shape
     elif isinstance(observation_space, spaces.Dict):
         return {key: get_obs_shape(subspace) for (key, subspace) in observation_space.spaces.items()}  # type: ignore[misc]
-
+    elif isinstance(observation_space, spaces.Graph):
+        return {key: get_obs_shape(subspace) for (key, subspace) in observation_space.spaces.items()}
     else:
         raise NotImplementedError(f"{observation_space} observation space is not supported")
 
diff --git a/stable_baselines3/common/type_aliases.py b/stable_baselines3/common/type_aliases.py
index d38d7cf73..2c08a4062 100644
--- a/stable_baselines3/common/type_aliases.py
+++ b/stable_baselines3/common/type_aliases.py
@@ -7,6 +7,7 @@
 import gymnasium as gym
 import numpy as np
 import torch as th
+from torch_geometric.data import Batch
 
 if sys.version_info >= (3, 8):
     from typing import Protocol
@@ -39,6 +40,15 @@ class RolloutBufferSamples(NamedTuple):
     returns: th.Tensor
 
 
+class GraphRolloutBufferSamples(NamedTuple):
+    observations: Batch
+    actions: th.Tensor
+    old_values: th.Tensor
+    old_log_prob: th.Tensor
+    advantages: th.Tensor
+    returns: th.Tensor
+
+
 class DictRolloutBufferSamples(NamedTuple):
     observations: TensorDict
     actions: th.Tensor
diff --git a/stable_baselines3/common/utils.py b/stable_baselines3/common/utils.py
index 08366bda1..7e1c2c5f4 100644
--- a/stable_baselines3/common/utils.py
+++ b/stable_baselines3/common/utils.py
@@ -13,6 +13,7 @@
 import numpy as np
 import torch as th
 from gymnasium import spaces
+from torch_geometric.data import Data
 
 import stable_baselines3 as sb3
 
@@ -482,6 +483,8 @@ def obs_as_tensor(obs: Union[np.ndarray, Dict[str, np.ndarray]], device: th.devi
     """
     if isinstance(obs, np.ndarray):
         return th.as_tensor(obs, device=device)
+    elif isinstance(obs, Data):
+        return obs.to(device)
     elif isinstance(obs, dict):
         return {key: th.as_tensor(_obs, device=device) for (key, _obs) in obs.items()}
     else:
diff --git a/stable_baselines3/common/vec_env/__init__.py b/stable_baselines3/common/vec_env/__init__.py
index 2c036373a..3f35fecae 100644
--- a/stable_baselines3/common/vec_env/__init__.py
+++ b/stable_baselines3/common/vec_env/__init__.py
@@ -3,7 +3,7 @@
 from typing import Optional, Type, Union
 
 from stable_baselines3.common.vec_env.base_vec_env import CloudpickleWrapper, VecEnv, VecEnvWrapper
-from stable_baselines3.common.vec_env.dummy_vec_env import DummyVecEnv
+from stable_baselines3.common.vec_env.dummy_vec_env import DummyVecEnv, DummyGraphVecEnv
 from stable_baselines3.common.vec_env.stacked_observations import StackedObservations
 from stable_baselines3.common.vec_env.subproc_vec_env import SubprocVecEnv
 from stable_baselines3.common.vec_env.vec_check_nan import VecCheckNan
diff --git a/stable_baselines3/common/vec_env/dummy_vec_env.py b/stable_baselines3/common/vec_env/dummy_vec_env.py
index 822025f53..0242629b9 100644
--- a/stable_baselines3/common/vec_env/dummy_vec_env.py
+++ b/stable_baselines3/common/vec_env/dummy_vec_env.py
@@ -8,7 +8,7 @@
 
 from stable_baselines3.common.vec_env.base_vec_env import VecEnv, VecEnvIndices, VecEnvObs, VecEnvStepReturn
 from stable_baselines3.common.vec_env.patch_gym import _patch_env
-from stable_baselines3.common.vec_env.util import copy_obs_dict, dict_to_obs, obs_space_info
+from stable_baselines3.common.vec_env.util import graph_copy_obs_dict, copy_obs_dict, dict_to_obs, obs_space_info
 
 
 class DummyVecEnv(VecEnv):
@@ -24,8 +24,6 @@ class DummyVecEnv(VecEnv):
     :raises ValueError: If the same environment instance is passed as the output of two or more different env_fn.
     """
 
-    actions: np.ndarray
-
     def __init__(self, env_fns: List[Callable[[], gym.Env]]):
         self.envs = [_patch_env(fn()) for fn in env_fns]
         if len(set([id(env.unwrapped) for env in self.envs])) != len(self.envs):
@@ -40,13 +38,14 @@ def __init__(self, env_fns: List[Callable[[], gym.Env]]):
             )
         env = self.envs[0]
         VecEnv.__init__(self, len(env_fns), env.observation_space, env.action_space, env.render_mode)
-        obs_space = env.observation_space
-        self.keys, shapes, dtypes = obs_space_info(obs_space)
+        self.obs_space = env.observation_space
+        self.keys, shapes, dtypes = obs_space_info(self.obs_space)
 
         self.buf_obs = OrderedDict([(k, np.zeros((self.num_envs, *tuple(shapes[k])), dtype=dtypes[k])) for k in self.keys])
         self.buf_dones = np.zeros((self.num_envs,), dtype=bool)
         self.buf_rews = np.zeros((self.num_envs,), dtype=np.float32)
         self.buf_infos: List[Dict[str, Any]] = [{} for _ in range(self.num_envs)]
+        self.actions = None
         self.metadata = env.metadata
 
     def step_async(self, actions: np.ndarray) -> None:
@@ -146,3 +145,20 @@ def env_is_wrapped(self, wrapper_class: Type[gym.Wrapper], indices: VecEnvIndice
     def _get_target_envs(self, indices: VecEnvIndices) -> List[gym.Env]:
         indices = self._get_indices(indices)
         return [self.envs[i] for i in indices]
+
+
+class DummyGraphVecEnv(DummyVecEnv):
+    def __init__(self, env_fns: List[Callable[[], gym.Env]]):
+        super().__init__(env_fns)
+        assert isinstance(self.obs_space, gym.spaces.Graph)
+        self.buf_obs = OrderedDict([(k, {}) for k in self.keys])
+
+    def _obs_from_buf(self) -> VecEnvObs:
+        assert isinstance(self.observation_space, gym.spaces.Graph)
+        return dict_to_obs(self.observation_space, graph_copy_obs_dict(self.buf_obs))
+
+    def _save_obs(self, env_idx: int, obs: VecEnvObs) -> None:
+        assert isinstance(self.envs[env_idx].observation_space, gym.spaces.Graph)
+        self.buf_obs["node"][env_idx] = obs.x
+        self.buf_obs["edge_weight"][env_idx] = obs.w
+        self.buf_obs["edge_index"][env_idx] = obs.edge_index
diff --git a/stable_baselines3/common/vec_env/util.py b/stable_baselines3/common/vec_env/util.py
index 2a03d8e70..241e67a33 100644
--- a/stable_baselines3/common/vec_env/util.py
+++ b/stable_baselines3/common/vec_env/util.py
@@ -3,6 +3,7 @@
 """
 from collections import OrderedDict
 from typing import Any, Dict, List, Tuple
+from torch_geometric.data import Data, Batch
 
 import numpy as np
 from gymnasium import spaces
@@ -22,6 +23,17 @@ def copy_obs_dict(obs: Dict[str, np.ndarray]) -> Dict[str, np.ndarray]:
     return OrderedDict([(k, np.copy(v)) for k, v in obs.items()])
 
 
+def graph_copy_obs_dict(obs: Dict[str, np.ndarray]) -> Dict[str, np.ndarray]:
+    """
+    Deep-copy a dict of numpy arrays.
+
+    :param obs: a dict of numpy arrays.
+    :return: a dict of copied numpy arrays.
+    """
+    assert isinstance(obs, OrderedDict), f"unexpected type for observations '{type(obs)}'"
+    return OrderedDict([(k, {i: env.clone() for i, env in v.items()}) for k, v in obs.items()])
+
+
 def dict_to_obs(obs_space: spaces.Space, obs_dict: Dict[Any, np.ndarray]) -> VecEnvObs:
     """
     Convert an internal representation raw_obs into the appropriate type
@@ -38,6 +50,12 @@ def dict_to_obs(obs_space: spaces.Space, obs_dict: Dict[Any, np.ndarray]) -> Vec
     elif isinstance(obs_space, spaces.Tuple):
         assert len(obs_dict) == len(obs_space.spaces), "size of observation does not match size of observation space"
         return tuple(obs_dict[i] for i in range(len(obs_space.spaces)))
+    elif isinstance(obs_space, spaces.Graph):
+        indexes = obs_dict["node"].keys()
+        list_of_graphs = [
+            Data(x=obs_dict["node"][i], edge_index=obs_dict["edge_index"][i], w=obs_dict["edge_weight"][i]) for i in indexes
+        ]
+        return Batch.from_data_list(list_of_graphs)
     else:
         assert set(obs_dict.keys()) == {None}, "multiple observation keys for unstructured observation space"
         return obs_dict[None]
@@ -63,6 +81,8 @@ def obs_space_info(obs_space: spaces.Space) -> Tuple[List[str], Dict[Any, Tuple[
         subspaces = obs_space.spaces
     elif isinstance(obs_space, spaces.Tuple):
         subspaces = {i: space for i, space in enumerate(obs_space.spaces)}  # type: ignore[assignment]
+    elif isinstance(obs_space, spaces.Graph):
+        subspaces = obs_space.spaces
     else:
         assert not hasattr(obs_space, "spaces"), f"Unsupported structured space '{type(obs_space)}'"
         subspaces = {None: obs_space}  # type: ignore[assignment]