Reviewer has chosen to be Anonymous

Summary of paper in a few sentences:

I have reviewed your manuscript titled: "Heterogeneous Multi-layered Network for Modeling Complex Graph-Data." Your work represents a compelling approach towards integrating heterogeneity and multi-layered properties of networks, introducing an algorithm for generating synthetic networks and showing its generalizability across multiple data sources.

Reasons to accept:

The authors provide an innovative modelling approach that is of broader scientific significance and interest and the data sources are made publicly available for reproducibility.
Notably, various experiments with data sources spanning multiple domains are utilized to test for generalizability of their network approach that is situated with the scientific literature. The contribution is rigorously carved out and the results are presented in an adequate quality and elaboration degree.

Reasons to reject:

Below are some specific points of feedback that I believe will strengthen your paper:
Abstract:
You introduce the HMN as an abbreviation, please refer to the generalized network model in the same way for better clarity. Please provide an example of the structural measures that you deliver.
You state that heterogeneous multi-layered networks (HMN) are more efficient, but the comparison lacks context. Specify the benchmark or state-of-the-art (SOTA) methods against which you are comparing your approach.
Explain the rationale behind choosing the Twitter network and air-transportation network as your use cases. What specific characteristics of these networks make them suitable for your research goals?
You conducted multiple experiments with various datasets (e.g., molecule dataset, brain networks) to prove generalizability. Clearly state the research question/hypothesis and corresponding methodological choices for these experiments
Section 4.1.1:
You use the MovieLens dataset for link prediction, which was not introduced earlier. Provide a clear introduction to the methods used and lay out all of the experiments beforehand to ensure coherence.
You mention "state-of-the-art GNN architectures available" (line 31, p.9) but do not specify which ones. Clarify this and explain why you chose to use t-SNE. Additionally, detail how you fine-tuned the hyperparameters of t-SNE.
Table Results:
Report the results presented in the tables (e.g. Table 4 and Table 5) within the text to ensure they are clearly contextualized.
Limitations Section:
Include a section discussing the limitations of your study to provide a balanced view and acknowledge areas for future research.
Figures:
Figure 2: Improve the interpretation. The text mentions "The first layer contains tweets and the second layer contains users," but it is unclear which layer is which in the figure.
Figure 3: The description says "with each rectangle representing a layer. The first layer contains tweets and the second layer contains users," but as a reader, I only see one layer (rectangle). You seem to express layers through edge types, which is challenging to understand. Clarify this representation.
Figure 5: This figure is never mentioned or discussed in the text. Ensure that every figure is referenced and discussed. Additionally, the captions of the subplots are too small to read, and the font differs from the rest of the manuscript. Ensure consistency in formatting.
Figure 6: The figure lacks an interpretation in the text. The caption does not adequately explain what subplots (a-d) specifically represent. Provide a detailed explanation in both the text and caption.

Nanopublication comments:

Further comments:

By Fabio Sartori https://orcid.org/0009-0006-5376-5631

Review Details

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Reviewer has chosen not to be Anonymous

Summary of paper in a few sentences:

The authors introduced a class of network they named "Heterogeneous Multilayer Networks" that allows to generate networks that contains both several layers and heterogeneity of nodes and edges.

Furthermore, they generalize several classical definitions such as degree centrality and betweenness centrality to that class of networks.

Finally they describe an algorithm to generate such networks, and compare the statistics of such network with some real-life networks.

Reasons to accept:

The manuscript provides a mathematical definition of HMN. The most similar result I found in the litterature is in [1], where only one type of node is allowed per layer. (One could reduce each network generated by the authors manuscript to a network as described in [1], but that would multiply the number of layers)

[1] Wan, Liangtian, et al. "Identification of important nodes in multilayer heterogeneous networks incorporating multirelational information." IEEE Transactions on Computational Social Systems 9.6 (2022): 1715-1724.

Reasons to reject:

The manuscript overall lack of care, background study, consistency, and clarity/motivation for the generation of Tables 2-6 and Figure 5

More in detail:
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The manuscript contains several extremely strong statements that are either false or conflicting with each other:
"A multi-layered network cannot support heterogeneity in a layer due to the absence of node or edge types." (Adding heterogeneity to layers is the main contribution of their manuscript)
"it is difficult to obtain heterogeneous multi-layered networks despite a lot of real-world networks being HMN" (contradicting what was said before, and easy to argue against it)
"except this work, there is no mention of heterogeneous multilayered networks in the literature" (from a quick search from Google Scholar, more than 200 papers contain the wording "multilayer heterogeneous network", [1] itself propose a framework very similar to the one described in the Manuscript, but they don't mention it, nor they explain why their model is better, or where it differs from it)

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The most problematic section is Section 7.
The authors introduced in Sec 6 an algorithm to generate HMN, and here they compare the network generated with their algorithm to real-life networks and show that their network is better suited to capture their characteristics compared to classical network generators. (Which is a lovely idea per se)
However, they fail to specify the parameters they used to generate the other network or why they chose such parameters. The result is an Erdos–Rènyi graph (they call it erdos-reyni) with a probability of connection p > 0.5, which leads to an average number of links per node above 10^4. I have more concerns about Figure 6: the degree distribution of an ER graph in a log-log scale should be extremely narrow, the one they generate is not shown in its entirety, and it's very flat, spanning an entire order of magnitude. The Barabasi-Albert degree distribution is not a power-law.

There is also a problem with inconsistencies in the labels. They are comparing their model to generate HMN with the TWITT dataset; in the plot, they refer to the TWITT dataset as "user-user", the network they generate is named "synthetic 20000" in the legend, and "synthetic" in the main body of the manuscript, the Erdos-Reny network is called "erdos-reyni", and "Internet as graph" in the main text became "random internet" in the figure legend.

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In Tables 2-5, the authors compared the network generated with their algorithm with several real-life networks. (I like the idea) But they fail even at generating networks with the same number of nodes. In table 2, for example, they generated both a HMN network and a BINBALL network to mimic the EATN network. The original network had 55 nodes and 97 edges, while the one they generated with their algorithm had 67 nodes and 208 edges, and the one generated with the classical model BINBALL had 106 nodes and 22 edges. Not only the BINBALL air network is not connected, but more than half of the airports (nodes) they generated have 0 connections with other airports.

Nanopublication comments:

Further comments: