From 2745470dd67e41a78491b6cebb1ef5aacf2a546d Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Fri, 8 Jul 2022 12:41:38 +0200
Subject: [PATCH 01/18] update error message of validate_adjacency

---
 src/torch_ppr/utils.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index 398d5cf..ef1939a 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -144,7 +144,9 @@ def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None):
         # hotfix until torch.sparse.sum is implemented
         adj_sum = adj.t() @ torch.ones(adj.shape[0])
     if not torch.allclose(adj_sum, torch.ones_like(adj_sum), rtol=1.0e-04):
-        raise ValueError(f"Invalid column sum: {adj_sum}. expected 1.0")
+        raise ValueError(
+            f"Invalid column sum: {adj_sum} (min: {adj_sum.min().item()}, max: {adj_sum.max().item()}). expected 1.0"
+        )
 
 
 def prepare_page_rank_adjacency(

From 92703e9541116e7fe56cadda234ffbdf198657ed Mon Sep 17 00:00:00 2001
From: Charles Tapley Hoyt <cthoyt@gmail.com>
Date: Fri, 8 Jul 2022 08:27:49 -0400
Subject: [PATCH 02/18] Update utils.py

---
 src/torch_ppr/utils.py | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index ef1939a..34cf342 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -95,7 +95,7 @@ def edge_index_to_sparse_matrix(
     )
 
 
-def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None):
+def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None, rtol: float = 1.0e-04):
     """
     Validate the page-rank adjacency matrix.
 
@@ -108,6 +108,8 @@ def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None):
         the adjacency matrix
     :param n:
         the number of nodes
+    :param rtol:
+        the tolerance for checking the sum is close to 1.0
 
     :raises ValueError:
         if the adjacency matrix is invalid
@@ -143,9 +145,9 @@ def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None):
     else:
         # hotfix until torch.sparse.sum is implemented
         adj_sum = adj.t() @ torch.ones(adj.shape[0])
-    if not torch.allclose(adj_sum, torch.ones_like(adj_sum), rtol=1.0e-04):
+    if not torch.allclose(adj_sum, torch.ones_like(adj_sum), rtol=rtol):
         raise ValueError(
-            f"Invalid column sum: {adj_sum} (min: {adj_sum.min().item()}, max: {adj_sum.max().item()}). expected 1.0"
+            f"Invalid column sum: {adj_sum} (min: {adj_sum.min().item()}, max: {adj_sum.max().item()}). expected 1.0 with a tolerance of {rtol}"
         )
 
 

From 66b8a4f605a3d988439ebfbb59864fc0a6050e43 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Fri, 8 Jul 2022 14:29:17 +0200
Subject: [PATCH 03/18] break line

---
 src/torch_ppr/utils.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index 34cf342..33a8d04 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -147,7 +147,8 @@ def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None, rtol: float =
         adj_sum = adj.t() @ torch.ones(adj.shape[0])
     if not torch.allclose(adj_sum, torch.ones_like(adj_sum), rtol=rtol):
         raise ValueError(
-            f"Invalid column sum: {adj_sum} (min: {adj_sum.min().item()}, max: {adj_sum.max().item()}). expected 1.0 with a tolerance of {rtol}"
+            f"Invalid column sum: {adj_sum} (min: {adj_sum.min().item()}, max: {adj_sum.max().item()}). "
+            f"Expected 1.0 with a relative tolerance of {rtol}.",
         )
 
 

From 99f242b0fe8bac4e77556bf1617f5eb19dd951f6 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 11 Jul 2022 18:23:36 +0200
Subject: [PATCH 04/18] add handling of isolated vertices

---
 src/torch_ppr/utils.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index 33a8d04..f111805 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -145,7 +145,12 @@ def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None, rtol: float =
     else:
         # hotfix until torch.sparse.sum is implemented
         adj_sum = adj.t() @ torch.ones(adj.shape[0])
-    if not torch.allclose(adj_sum, torch.ones_like(adj_sum), rtol=rtol):
+    exp_sum = torch.ones_like(adj_sum)
+    mask = adj_sum == 0
+    if mask.any():
+        logger.warning(f"Adjacency contains {mask.sum().item()} isolated nodes.")
+        exp_sum[mask] = 0.0
+    if not torch.allclose(adj_sum, exp_sum, rtol=rtol):
         raise ValueError(
             f"Invalid column sum: {adj_sum} (min: {adj_sum.min().item()}, max: {adj_sum.max().item()}). "
             f"Expected 1.0 with a relative tolerance of {rtol}.",

From 19a781fcb569c3621511b81773ec5165d5e5a6b6 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 11 Jul 2022 18:29:50 +0200
Subject: [PATCH 05/18] fix division-by-zero for isolated vertices

---
 src/torch_ppr/utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index f111805..d7870c5 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -198,7 +198,7 @@ def prepare_page_rank_adjacency(
     # symmetrize
     adj = adj + adj.t()
     # adjacency normalization: normalize to col-sum = 1
-    degree_inv = torch.reciprocal(torch.sparse.sum(adj, dim=0).to_dense())
+    degree_inv = torch.reciprocal(torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=1.0e-08))
     degree_inv = torch.sparse_coo_tensor(
         indices=torch.arange(degree_inv.shape[0], device=adj.device).unsqueeze(dim=0).repeat(2, 1),
         values=degree_inv,

From 37b37845a10a618292c6bceb25e66d20e8c05c3d Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 11 Jul 2022 18:30:25 +0200
Subject: [PATCH 06/18] add todo note

---
 src/torch_ppr/utils.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index d7870c5..a2e7c55 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -197,6 +197,7 @@ def prepare_page_rank_adjacency(
     adj = edge_index_to_sparse_matrix(edge_index=edge_index, num_nodes=num_nodes)
     # symmetrize
     adj = adj + adj.t()
+    # TODO: should we add an identity matrix here?
     # adjacency normalization: normalize to col-sum = 1
     degree_inv = torch.reciprocal(torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=1.0e-08))
     degree_inv = torch.sparse_coo_tensor(

From d66e61af0c90198f5b5fc2be1b5ee34d22280a6f Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Tue, 12 Jul 2022 09:29:11 +0200
Subject: [PATCH 07/18] use torch's eps

---
 src/torch_ppr/utils.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index a2e7c55..6bf9607 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -199,7 +199,9 @@ def prepare_page_rank_adjacency(
     adj = adj + adj.t()
     # TODO: should we add an identity matrix here?
     # adjacency normalization: normalize to col-sum = 1
-    degree_inv = torch.reciprocal(torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=1.0e-08))
+    degree_inv = torch.reciprocal(
+        torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=torch.finfo(dtype=adj.dtype).eps)
+    )
     degree_inv = torch.sparse_coo_tensor(
         indices=torch.arange(degree_inv.shape[0], device=adj.device).unsqueeze(dim=0).repeat(2, 1),
         values=degree_inv,

From 06f126a280cbdc978c1132a8fc51310ad1260e6b Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 09:47:09 +0200
Subject: [PATCH 08/18] do not use keyword

---
 src/torch_ppr/utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index 6bf9607..ca8cd75 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -200,7 +200,7 @@ def prepare_page_rank_adjacency(
     # TODO: should we add an identity matrix here?
     # adjacency normalization: normalize to col-sum = 1
     degree_inv = torch.reciprocal(
-        torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=torch.finfo(dtype=adj.dtype).eps)
+        torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=torch.finfo(adj.dtype).eps)
     )
     degree_inv = torch.sparse_coo_tensor(
         indices=torch.arange(degree_inv.shape[0], device=adj.device).unsqueeze(dim=0).repeat(2, 1),

From 330efec352b8ab340e6c2ca5293b01fb44835177 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 09:50:32 +0200
Subject: [PATCH 09/18] extract utility

---
 src/torch_ppr/utils.py | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index ca8cd75..e4f79de 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -157,6 +157,21 @@ def validate_adjacency(adj: torch.Tensor, n: Optional[int] = None, rtol: float =
         )
 
 
+def sparse_diagonal(values: torch.Tensor) -> torch.Tensor:
+    """Create a sparse diagonal matrix with the given values.
+
+    :param values: shape: ``(n,)``
+        the values
+
+    :return: shape: ``(n, n)``
+        a sparse diagonal matrix
+    """
+    return torch.sparse_coo_tensor(
+        indices=torch.arange(values.shape[0], device=values.device).unsqueeze(dim=0).repeat(2, 1),
+        values=values,
+    )
+
+
 def prepare_page_rank_adjacency(
     adj: Optional[torch.Tensor] = None,
     edge_index: Optional[torch.LongTensor] = None,
@@ -202,10 +217,7 @@ def prepare_page_rank_adjacency(
     degree_inv = torch.reciprocal(
         torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=torch.finfo(adj.dtype).eps)
     )
-    degree_inv = torch.sparse_coo_tensor(
-        indices=torch.arange(degree_inv.shape[0], device=adj.device).unsqueeze(dim=0).repeat(2, 1),
-        values=degree_inv,
-    )
+    degree_inv = sparse_diagonal(values=degree_inv)
     return torch.sparse.mm(adj, degree_inv)
 
 

From d456db2b693198e4711a732fa82ff4d37aee20da Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 09:51:56 +0200
Subject: [PATCH 10/18] add option to add identity matrix

---
 src/torch_ppr/utils.py | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index e4f79de..f616dbd 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -176,6 +176,7 @@ def prepare_page_rank_adjacency(
     adj: Optional[torch.Tensor] = None,
     edge_index: Optional[torch.LongTensor] = None,
     num_nodes: Optional[int] = None,
+    add_identity: bool = False,
 ) -> torch.Tensor:
     """
     Prepare the page-rank adjacency matrix.
@@ -195,6 +196,8 @@ def prepare_page_rank_adjacency(
     :param num_nodes:
         the number of nodes used to determine the shape of the adjacency matrix.
         If ``None``, and ``adj`` is not already provided, it is inferred from ``edge_index``.
+    :param add_identity:
+        whether to add an identity matrix to ``A`` to ensure that each node has a degree of at least one.
 
     :raises ValueError:
         if neither is provided, or the adjacency matrix is invalid
@@ -212,6 +215,9 @@ def prepare_page_rank_adjacency(
     adj = edge_index_to_sparse_matrix(edge_index=edge_index, num_nodes=num_nodes)
     # symmetrize
     adj = adj + adj.t()
+    if add_identity:
+        adj = adj + sparse_diagonal(torch.ones(adj.shape[0], dtype=adj.dtype, device=adj.device))
+
     # TODO: should we add an identity matrix here?
     # adjacency normalization: normalize to col-sum = 1
     degree_inv = torch.reciprocal(

From 8114025eabbc1669fa7b0845204dd5455723b260 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 09:55:32 +0200
Subject: [PATCH 11/18] expose to API

---
 src/torch_ppr/api.py | 16 ++++++++++++----
 1 file changed, 12 insertions(+), 4 deletions(-)

diff --git a/src/torch_ppr/api.py b/src/torch_ppr/api.py
index 4c875fa..7363d27 100644
--- a/src/torch_ppr/api.py
+++ b/src/torch_ppr/api.py
@@ -31,6 +31,7 @@ def page_rank(
     adj: Optional[torch.Tensor] = None,
     edge_index: Optional[torch.LongTensor] = None,
     num_nodes: Optional[int] = None,
+    add_identity: bool = False,
     max_iter: int = 1_000,
     alpha: float = 0.05,
     epsilon: float = 1.0e-04,
@@ -48,6 +49,8 @@ def page_rank(
     :param num_nodes:
         the number of nodes used to determine the shape of the adjacency matrix.
         If ``None``, and ``adj`` is not already provided, it is inferred from ``edge_index``.
+    :param add_identity:
+        whether to add an identity matrix to ``A`` to ensure that each node has a degree of at least one.
 
     :param max_iter: ``max_iter > 0``
         the maximum number of iterations
@@ -69,7 +72,9 @@ def page_rank(
         the page-rank vector, i.e., a score between 0 and 1 for each node.
     """
     # normalize inputs
-    adj = prepare_page_rank_adjacency(adj=adj, edge_index=edge_index, num_nodes=num_nodes)
+    adj = prepare_page_rank_adjacency(
+        adj=adj, edge_index=edge_index, num_nodes=num_nodes, add_identity=add_identity
+    )
     validate_adjacency(adj=adj)
 
     x0 = prepare_x0(x0=x0, n=adj.shape[0])
@@ -96,6 +101,7 @@ def personalized_page_rank(
     *,
     adj: Optional[torch.Tensor] = None,
     edge_index: Optional[torch.LongTensor] = None,
+    add_identity: bool = False,
     num_nodes: Optional[int] = None,
     indices: Optional[torch.Tensor] = None,
     device: DeviceHint = None,
@@ -115,6 +121,8 @@ def personalized_page_rank(
     :param num_nodes:
         the number of nodes used to determine the shape of the adjacency matrix.
         If ``None``, and ``adj`` is not already provided, it is inferred from ``edge_index``.
+    :param add_identity:
+        whether to add an identity matrix to ``A`` to ensure that each node has a degree of at least one.
 
     :param indices: shape: ``(k,)``
         the node indices for which to calculate the PPR. Defaults to all nodes.
@@ -131,9 +139,9 @@ def personalized_page_rank(
     # resolve device first
     device = resolve_device(device=device)
     # prepare adjacency and indices only once
-    adj = prepare_page_rank_adjacency(adj=adj, edge_index=edge_index, num_nodes=num_nodes).to(
-        device=device
-    )
+    adj = prepare_page_rank_adjacency(
+        adj=adj, edge_index=edge_index, num_nodes=num_nodes, add_identity=add_identity
+    ).to(device=device)
     validate_adjacency(adj=adj)
 
     if indices is None:

From 08cf1fd349ee751bdef99bff96f764b80e1cceb9 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 09:59:05 +0200
Subject: [PATCH 12/18] add test for sparse diagonal

---
 tests/test_utils.py | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/tests/test_utils.py b/tests/test_utils.py
index 5fe0f24..9d16fb9 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -6,6 +6,7 @@
 from torch.nn import functional
 
 from torch_ppr import utils
+import pytest
 
 
 def test_resolve_device():
@@ -165,3 +166,14 @@ def test_batched_personalized_page_rank(self):
             adj=self.adj, indices=torch.arange(self.num_nodes), batch_size=self.num_nodes // 3
         )
         utils.validate_x(x)
+
+
+@pytest.mark.parametrize("n", [8, 16])
+def test_sparse_diagonal(n: int):
+    """Test for sparse diagonal matrix creation."""
+    values = torch.rand(n)
+    matrix = utils.sparse_diagonal(values=values)
+    assert torch.is_tensor(matrix)
+    assert matrix.shape == (n, n)
+    assert matrix.is_sparse
+    assert torch.allclose(matrix.to_dense(), torch.diag(values))

From cd6d420aaf760acf0d757991a88f43d13c7148f3 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 10:00:51 +0200
Subject: [PATCH 13/18] test add identity

---
 tests/test_utils.py | 18 +++++++++++++-----
 1 file changed, 13 insertions(+), 5 deletions(-)

diff --git a/tests/test_utils.py b/tests/test_utils.py
index 9d16fb9..5c464d2 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -100,14 +100,18 @@ def test_validate_adjacancy(self):
 
     def test_prepare_page_rank_adjacency(self):
         """Test adjacency preparation."""
-        for (adj, edge_index) in (
+        for (adj, edge_index, add_identity) in (
             # from edge index
-            (None, self.edge_index),
+            (None, self.edge_index, False),
             # passing through adjacency matrix
-            (self.adj, None),
-            (self.adj, self.edge_index),
+            (self.adj, None, False),
+            (self.adj, self.edge_index, False),
+            # add identity
+            (None, self.edge_index, True),
         ):
-            adj2 = utils.prepare_page_rank_adjacency(adj=adj, edge_index=edge_index)
+            adj2 = utils.prepare_page_rank_adjacency(
+                adj=adj, edge_index=edge_index, add_identity=add_identity
+            )
             utils.validate_adjacency(adj=adj2, n=self.num_nodes)
             if adj is not None:
                 assert adj is adj2
@@ -177,3 +181,7 @@ def test_sparse_diagonal(n: int):
     assert matrix.shape == (n, n)
     assert matrix.is_sparse
     assert torch.allclose(matrix.to_dense(), torch.diag(values))
+
+
+def test_a():
+    utils.prepare_page_rank_adjacency()

From 2030c2e3e2505af87ca8d94544098d3151de6769 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 10:01:26 +0200
Subject: [PATCH 14/18] remove artifact

---
 tests/test_utils.py | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/tests/test_utils.py b/tests/test_utils.py
index 5c464d2..e30078f 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -181,7 +181,3 @@ def test_sparse_diagonal(n: int):
     assert matrix.shape == (n, n)
     assert matrix.is_sparse
     assert torch.allclose(matrix.to_dense(), torch.diag(values))
-
-
-def test_a():
-    utils.prepare_page_rank_adjacency()

From d586b3b6a031ecd5a64d5e8a9b02a71755cc1830 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Mon, 18 Jul 2022 10:03:57 +0200
Subject: [PATCH 15/18] reformat

---
 tests/test_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/test_utils.py b/tests/test_utils.py
index e30078f..a934bec 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -2,11 +2,11 @@
 import unittest
 from typing import Counter, Optional, Tuple
 
+import pytest
 import torch
 from torch.nn import functional
 
 from torch_ppr import utils
-import pytest
 
 
 def test_resolve_device():

From 44f4f2e8132ab4cad85890d4489176696b9883dc Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Wed, 20 Jul 2022 11:18:30 +0200
Subject: [PATCH 16/18] fix outdated TODO note

---
 src/torch_ppr/utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/torch_ppr/utils.py b/src/torch_ppr/utils.py
index f616dbd..4efc931 100644
--- a/src/torch_ppr/utils.py
+++ b/src/torch_ppr/utils.py
@@ -215,10 +215,10 @@ def prepare_page_rank_adjacency(
     adj = edge_index_to_sparse_matrix(edge_index=edge_index, num_nodes=num_nodes)
     # symmetrize
     adj = adj + adj.t()
+    # add identity matrix if requested
     if add_identity:
         adj = adj + sparse_diagonal(torch.ones(adj.shape[0], dtype=adj.dtype, device=adj.device))
 
-    # TODO: should we add an identity matrix here?
     # adjacency normalization: normalize to col-sum = 1
     degree_inv = torch.reciprocal(
         torch.sparse.sum(adj, dim=0).to_dense().clamp_min(min=torch.finfo(adj.dtype).eps)

From 58b7a64b96e25c5b47663da535dcba124c200acb Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Wed, 20 Jul 2022 11:25:00 +0200
Subject: [PATCH 17/18] add test for isolated vertex handling

---
 tests/test_api.py | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/tests/test_api.py b/tests/test_api.py
index 8904069..3ca75fc 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -50,3 +50,16 @@ def test_page_rank_manual(self):
         x = page_rank(edge_index=edge_index)
         # verify that central node has the largest PR value
         assert x.argmax() == 1
+
+    def test_page_rank_isolated_vertices(self):
+        """Test Page-Rank with isolated vertices."""
+        # create isolated node, ID=0
+        edge_index = self.edge_index + 1
+        x = page_rank(edge_index=edge_index, add_identity=True)
+        # isolated node has only one self-loop -> no change in mass to initial mass
+        self.assertAlmostEqual(x[0].item(), 1 / (self.num_nodes + 1))
+        # verify that other nodes are unaffected
+        x2 = page_rank(edge_index=self.edge_index)
+        # rescale
+        x2 = x2 * (self.num_nodes / (self.num_nodes + 1))
+        assert torch.allclose(x2, x[1:], atol=1.0e-02)

From 1b4b6049b3f041be4d468d12e97b81082dde9266 Mon Sep 17 00:00:00 2001
From: Max Berrendorf <berrendorf@dbs.ifi.lmu.de>
Date: Wed, 20 Jul 2022 11:25:26 +0200
Subject: [PATCH 18/18] fix seed for reproducible tests

---
 tests/test_api.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/tests/test_api.py b/tests/test_api.py
index 3ca75fc..19d9cd2 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -15,9 +15,12 @@ class APITest(unittest.TestCase):
 
     def setUp(self) -> None:
         """Prepare data."""
+        generator = torch.manual_seed(42)
         self.edge_index = torch.cat(
             [
-                torch.randint(self.num_nodes, size=(2, self.num_edges - self.num_nodes)),
+                torch.randint(
+                    self.num_nodes, size=(2, self.num_edges - self.num_nodes), generator=generator
+                ),
                 # ensure connectivity
                 torch.arange(self.num_nodes).unsqueeze(0).repeat(2, 1),
             ],