Reviewer has chosen to be Anonymous

Overall Impression: Good

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes
Adequacy of the bibliography: Yes, but see detailed comments

Presentation:
Adequacy of the abstract: Yes
Introduction: background and motivation: Good
Organization of the paper: Satisfactory
Level of English: Satisfactory
Overall presentation: Good

Detailed Comments:

Title: Experiments in Graph Structure and Knowledge Graph Embeddings

Summary:

This paper analyzes the impact of adding additional information to
knowledge graphs on link prediction tasks. The contributions also
include new datasets and mechanisms to extend knowledge graphs. The
evaluation is carried out over several knowledge graph embeddings.

Strengths:

- The paper is well motivated and the objectives of the study are
clearly stated.

- The work provides new datasets that can be of interest of the
community.

Comments:

- I have a major comment about the KGE methods chosen for evaluation
of link prediction. While the evaluation considers many knowledge
graph embedding methods such as TransE, ComplEx, DistMult, RESCAL,
RotatE, I think these methods cannot leverage the new information
added in the extended knowledge graphs. For example, authors
acknowledge that "relations P31 and P279 are not symmetric; therefore
DistMult, which can encode symmetric relations, cannot leverage P31
and P279 edges". Following this line of reasoning, P279 (subclassof) is a
hierarchical relation, which should be evaluated with methods that
can encode hierarchies such as https://arxiv.org/pdf/1911.09419 or
https://link.springer.com/article/10.1007/s00521-024-09775-y. Also
in the case of P31 relation, it is well known that it is a N-1
relation, therefore a method encoding N-1 relations (such as TransD)
should be chosen for this property. In summary, I think the
evaluation does not match the hypothesis the authors intend to
propose.

Minor comments:

- While Fig. 1 is very useful, it is not self-explainable. Maybe
adding edge labels such as "type_of" of "subclass_of" and adding a
richer caption can help to improve this figure. So far, we need to
go back to the introduction to read about the difference between
each isotope.

- Section 3.5 point (d): t-sne and umap should be t-SNE and UMAP maybe?

- There are several references pointing to ArXiv while published versions of
those papers exist. I think that should be corrected.

Reviewer has chosen not to be Anonymous

Overall Impression: Average

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes
Adequacy of the bibliography: Yes

Presentation:
Adequacy of the abstract: Yes
Introduction: background and motivation: Limited
Organization of the paper: Needs improvement
Level of English: Satisfactory
Overall presentation: Average

Detailed Comments:

The paper presents experiments to analyze whether the presence in a KG impacts the performance of KGE algorithms. It does so by introducing synthetic datasets, each corresponding to a certain pattern of semantic information, and analyzing the influences of these patterns independently.
Then, it proposes to analyze qualitatively if semantic properties correlate with structural properties of the embeddings by analyzing a series of visualizations of the embeddings.

Overall I found that the paper has good motivations and technical qualities, but that it could really improve by reworking its presentation in some of the sections.

Strengths:
S1. The paper has good motivations,
S2. The experimental setup is well detailed,
S3. The quantitative results are well-organized.

Weaknesses:
W1. The introduction of the synthetic datasets in the Introduction and Section 3 needs better contextualization. I guess the synthetic data somehow tries to replicate real-world data patterns, to be insightful. It would be interesting to add examples for each of the SKG graphs introduced for the reader to understand what they could represent in reality.
W2. Similarly, I didn't understand the motivation for SKG-237. Other than having a similar number of nodes and degrees with FB15k-237, does it replicate any important structural patterns? If the patterns are just random, then isn't it naturally expected that performance is bad on it? In that case, I find that it doesn't add much to the insights and the story would be clearer without it. If it does replicate important patterns, please clarify and elaborate Section 3.3 (too short at the moment).
W3. I find the discussions of KGE performance over SKG isotopes (in Section 5.1), which seems to be the main story of the paper, too brief. The last paragraph cuts in the middle, so I wonder if there may have been a problem with the submission.
W4. Another concern is that the second contribution, on the visual analysis of the embeddings, is impossible to review because it is present only in appendix and not attached to the submission. If the authors submit a revision, please include the appendix, or at least include the most important Figure in the main paper (since it is even part of the abstract).

Questions:
Q1. I don't understand how it's possible to create dataset splits for KGEs on let's say SKG-4, if you explain in Section 3 that they all have disconnected components. For SKG-4, every single triple has an object with a node degree of 1. If you put any triple in valid/test, then it means that its object will never seen in training. But KGE methods are designed for transductive link prediction; their results will be random for nodes that are never seen in training. How did you manage the splits?
Q2. Table 6: How are the degree centrality values computed? Maybe I'm using the wrong concept, but I thought it would be the number of edges (in or out) connecting to a node. Then doesn't the graph in SKG4 have at least 1 edge connecting to each node? Same question for the other graphs. I expected the average degree to then be greater than 1.0, I don't understand how the values 0.003 etc. are obtained
Q3. Table 6: What does the difference column represent?

Minor comments:
- I think Figure 1 could be more clear by adding types on the edges that are different. For example, right now, for SKG5 it is stated that "the lavender property is always attached to the top node". But it's not explicit what defines a "top node" (graphs don't have orientations); I assume what defines it is the type of the edge.
- Figure 2 caption cuts in the middle.
- Section 5.2, line 50: In fact DistMult can ONLY represent symmetric relationships, since its score function cannot model asymmetry.