diff --git a/gklearn/ged/model/ged_model.py b/gklearn/ged/model/ged_model.py
index eb3f6afc8b..ea6793f04c 100644
--- a/gklearn/ged/model/ged_model.py
+++ b/gklearn/ged/model/ged_model.py
@@ -200,7 +200,13 @@ def transform(
 		return dis_matrix
 
 
-	def fit_transform(self, X, y=None, save_dm_train=False, **kwargs):
+	def fit_transform(
+			self,
+			X,
+			y=None,
+			save_dm_train=False,
+			save_mm_train: bool = False,
+			**kwargs):
 		"""Fit and transform: compute GED distance matrix on the same data.
 
 		Parameters
@@ -230,7 +236,7 @@ def fit_transform(self, X, y=None, save_dm_train=False, **kwargs):
 		#			finally:
 		#				np.seterr(**old_settings)
 
-		if save_dm_train:
+		if save_mm_train or save_dm_train:
 			self._dm_train = dis_matrix
 		# If the model is refitted and the `save_dm_train` flag is not set, then
 		# remove the previously computed dm_train to prevent conflicts.
@@ -270,6 +276,10 @@ def validate_parameters(self):
 		None.
 
 		"""
+		if self.parallel == False:
+			self.parallel = None
+		elif self.parallel == True:
+			self.parallel = 'imap_unordered'
 		if self.parallel is not None and self.parallel != 'imap_unordered':
 			raise ValueError('Parallel mode is not set correctly.')
 
@@ -316,25 +326,27 @@ def compute_distance_matrix(self, Y=None, **kwargs):
 		Parameters
 		----------
 		Y : list of graphs, optional
-			The target graphs. The default is None. If None kernel is computed
+			The target graphs. The default is None. If None distance is computed
 			between X and itself.
 
 		Returns
 		-------
-		kernel_matrix : numpy array, shape = [n_targets, n_inputs]
-			The computed kernel matrix.
+		dis_matrix : numpy array, shape = [n_targets, n_inputs]
+			The computed distance matrix.
 
 		"""
 		if Y is None:
-			# Compute Gram matrix for self._graphs (X).
+			# Compute metric matrix for self._graphs (X).
 			dis_matrix = self._compute_X_distance_matrix(**kwargs)
 		#			self._gram_matrix_unnorm = np.copy(self._gram_matrix)
 
 		else:
-			# Compute kernel matrix between Y and self._graphs (X).
+			# Compute metric matrix between Y and self._graphs (X).
 			Y_copy = ([g.copy() for g in Y] if self.copy_graphs else Y)
-			graphs_copy = ([g.copy() for g in
-			                self._graphs] if self.copy_graphs else self._graphs)
+			graphs_copy = (
+				[g.copy() for g in self._graphs]
+				if self.copy_graphs else self._graphs
+			)
 
 			start_time = time.time()
 
@@ -786,8 +798,8 @@ def is_graph(self, graph):
 		if isinstance(graph, nx.MultiDiGraph):
 			return True
 		return False
-	
-	
+
+
 	def __repr__(self):
 		return (
 			f"{self.__class__.__name__}("
@@ -833,20 +845,31 @@ def graphs(self):
 	def run_time(self):
 		return self._run_time
 
+
 	@property
 	def test_run_time(self):
 		return self._test_run_time
 
+
 	@property
 	def dis_matrix(self):
 		return self._dm_train
 
-
 	@dis_matrix.setter
 	def dis_matrix(self, value):
 		self._dm_train = value
 
 
+	@property
+	def metric_matrix(self):
+		return self._dm_train
+
+
+	@metric_matrix.setter
+	def metric_matrix(self, value):
+		self._dm_train = value
+
+
 	@property
 	def edit_cost_constants(self):
 		return self._edit_cost_constants
@@ -860,6 +883,17 @@ def edit_cost_constants(self):
 # 	def gram_matrix_unnorm(self, value):
 # 		self._gram_matrix_unnorm = value
 
+	@property
+	def n_pairs(self):
+		"""
+		The number of pairs of graphs between which the GEDs are computed.
+		"""
+		try:
+			check_is_fitted(self, '_dm_train')
+			return len(self._dm_train) * (len(self._dm_train) - 1) / 2
+		except NotFittedError:
+			return None
+
 
 def _init_worker_ged_mat(gn_toshare):
 	global G_gn
diff --git a/gklearn/kernels/graph_kernel.py b/gklearn/kernels/graph_kernel.py
index 7992396942..3a9ae9fa1f 100644
--- a/gklearn/kernels/graph_kernel.py
+++ b/gklearn/kernels/graph_kernel.py
@@ -154,7 +154,12 @@ def transform(self, X=None, load_gm_train=False):
 		return kernel_matrix
 
 
-	def fit_transform(self, X, save_gm_train=False):
+	def fit_transform(
+			self,
+			X,
+			save_gm_train: bool = False,
+			save_mm_train: bool = False,
+	):
 		"""Fit and transform: compute Gram matrix on the same data.
 
 		Parameters
@@ -187,7 +192,7 @@ def fit_transform(self, X, save_gm_train=False):
 			finally:
 				np.seterr(**old_settings)
 
-		if save_gm_train:
+		if save_mm_train or save_gm_train:
 			self._gm_train = gram_matrix
 
 		return gram_matrix
@@ -783,6 +788,16 @@ def gram_matrix(self, value):
 		self._gm_train = value
 
 
+	@property
+	def metric_matrix(self):
+		return self._gm_train
+
+
+	@metric_matrix.setter
+	def metric_matrix(self, value):
+		self._gm_train = value
+
+
 	@property
 	def gram_matrix_unnorm(self):
 		return self._gram_matrix_unnorm
@@ -791,3 +806,15 @@ def gram_matrix_unnorm(self):
 	@gram_matrix_unnorm.setter
 	def gram_matrix_unnorm(self, value):
 		self._gram_matrix_unnorm = value
+
+
+	@property
+	def n_pairs(self):
+		"""
+		The number of pairs of graphs between which the kernels are computed.
+		"""
+		try:
+			check_is_fitted(self, '_gm_train')
+			return len(self._gm_train) * (len(self._gm_train) + 1) / 2
+		except NotFittedError:
+			return None