Reviewer has chosen not to be Anonymous
Overall Impression: Bad
Suggested Decision: Reject
Technical Quality of the paper: Bad
Presentation: Bad
Reviewer`s confidence: High
Significance: Low significance
Background: Incomplete or inappropriate
Novelty: Limited novelty
Data availability: All used and produced data (if any) are FAIR and openly available in established data repositories
Length of the manuscript: The length of this manuscript is about right
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:
1 Comment
meta-review by editor
Submitted by Tobias Kuhn on
We have received two very detailed reviews. The first reviewer is positive but indicated a low confidence. The comments are pointing to unclear text sections and missing information. The second reviewer raises serveral fundamental concerns that require much attention. I advice you to address these points in great detail.
Michael Maes (https://orcid.org/0000-0001-9416-3211)