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Time evolution of the hierarchical networks between PubMed MeSH terms

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read New MeSH links attach by preference, not chance; child-rich nodes are favoured while high-ancestor nodes are avoided.

desk verdict A genuinely useful empirical study of how MeSH hierarchies grow and rewire, with a real but addressable statistical problem: the error bars assume independence across events that actually arrive in curator batches. read the letter →

arxiv 1908.10214 v1 pith:NMEN273P submitted 2019-08-27 physics.soc-ph cs.DLphysics.data-an

Sámuel G. Balogh , Dániel Zagyva , Péter Pollner , Gergely Palla This is my paper · ORCID
classification physics.soc-phcs.DLphysics.data-an PACS 89.75.Hc89.75.Fb
keywords MeSHhierarchiespreferentialattachmentnetworkevolutiondirectedacyclicgraphslinkdeletionrewiringPubMedtaxonomyrestructuring
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses the yearly public updates of the 16 MeSH hierarchies behind PubMed to ask whether the addition and deletion of links in a hierarchical network is random or biased. It finds that new links pointing from existing terms to newly introduced terms select source nodes with many children at a rate far above uniform chance, and that link deletion also favours nodes with many children and many descendants. At the same time, the total number of ancestors of a source node is avoided in essentially every type of link change, so shallow terms near the root are under-used as origins of restructuring. The authors conclude that rewiring and deletion matter as much as growth, and that hierarchy evolution mixes preferential and anti-preferential attachment over several topological properties at once.

What carries the argument

The carrying device is the ratio $W(x)=w(x)/Q(x)$, in which $Q(x)$ is the complementary cumulative distribution of a node property $x$ (number of children, parents, descendants, or ancestors) among available nodes, and $w(x)$ is the number of actually chosen nodes whose property is at least $x$. Under uniform random choice $W(x)$ is flat, an increasing $W(x)$ signals preference for large $x$, and a decreasing $W(x)$ signals anti-preference; the expected value and standard deviation of $W(x)$ are derived from a binomial model (Eq. 2) and used as error bands around the neutral value $W_{\mathrm{rand}}(x)$. For deletions the null model is selecting a uniformly random link, implemented by re-weighting $Q(x)$ by node degree, so that hubs are not mistakenly counted as preferred.

What would settle it

Run the same preference analysis with a null model that reshuffles which existing nodes are edited within each yearly update while preserving the number and type of edits, and check whether the strong preference for child-rich sources and the anti-preference for ancestor-rich sources remain outside the widened confidence intervals; a negative answer would overturn the central claim.

Watch

Extended reading notes

Core claim

The central discovery is that the growth and restructuring of the MeSH hierarchies are not uniformly random. When a new link is added from an old node to a new term, source nodes with more children are chosen with significantly higher probability than uniform random selection would give; deletion events likewise strike nodes with many children and many descendants. Conversely, the total number of ancestors of the source node displays anti-preference across nearly all change types, meaning broad, shallow terms are less likely than chance to be the origin of a rewiring or a new link. Properties of the target node have a smaller influence than properties of the source node, and across the seven largest hierarchies the same combination of change type and property never shows preference in one hierarchy and anti-preference in another. The authors present these patterns as evidence that taxonomy evolution is shaped by an interplay of multiple non-uniform, hierarchy-specific attachment rules rather than by a single preferential-attachment law.

Load-bearing premise

The binomial error model in Eq. (2) treats every link addition and deletion as an independent Bernoulli trial with a fixed probability $u(x)$, so if MeSH updates are applied as coordinated batches by curators, the error bands around $W_{\mathrm{rand}}$ are too narrow and some apparent preferences could be false positives.

Editorial extensions

If this is right

  • Deletion and rewiring between old nodes occur at the same magnitude as links to new nodes, so realistic models of hierarchy evolution must treat restructuring as a first-order process, not a perturbation.
  • A single preferential-attachment rule cannot explain the data; predicting where the next change lands requires simultaneous preferences over out-degree, descendant count, and ancestor count.
  • The anti-preference for high ancestor counts implies that reorganisation concentrates at intermediate depth, so future growth models should include a depth penalty for parent choice.
  • Because no hierarchy displays the opposite preference on the same cell, the qualitative pattern is generalisable across the largest MeSH hierarchies and plausibly to curated hierarchies elsewhere.
  • Source-node properties dominate target-node properties, so early indicators of upcoming rewiring should be measured on the parent side of a link.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The observed anti-preference for ancestor count may reflect curator intent to place new terms under the most specifically relevant existing parent, so the pattern could be an emergent signature of expertise-driven classification rather than a purely structural law.
  • If year-by-year edits are applied in coordinated batches, the independent-Bernoulli error bands in Eq. (7) are too narrow; a year-level permutation test would tell which reported preferences are robust to batch structure.
  • The same $W(x)$ statistic can be exported to other curated hierarchies such as gene ontology or Wikipedia category trees, offering a direct test of whether organised knowledge systems share this preference pattern.
  • A generative model linking parent choice to a power of child count multiplied by a decreasing function of depth could reproduce the joint pattern; fitting that function would turn the present qualitative findings into a quantitative evolution rule.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies the temporal evolution of the hierarchical networks formed by PubMed MeSH terms. Using yearly snapshots of 16 hierarchies (and 7 hierarchies with more than 1000 nodes during the whole period), the authors classify link changes into five types: additions involving old/new sources and targets, and deletions between old nodes. For each change type and for four node properties (number of children, number of parents, total descendants, total ancestors), they compare the observed complementary cumulative distribution of selected nodes against a random null model, computing W_emp(x) and comparing it to W_rand(x) plus or minus a binomial standard deviation. The central finding is that attachment events preferentially select source nodes with many children and many descendants, while the number of ancestors of the source node shows anti-preference across essentially all link-change types; deletion events also preferentially strike nodes with many children and descendants. The authors aggregate per-hierarchy classifications into a summary table and argue that the observed preferences are consistent across hierarchies.

Significance. If the statistical results hold, the paper provides a useful empirical characterization of how a large curated hierarchical ontology evolves, with concrete evidence that restructuring is not uniform but is biased by topological and hierarchical node properties. The analysis uses publicly available data, the methodology is transparent, and the authors validate the W(x) framework on simulated attachment events, which are strengths. The claimed preferences are potentially relevant for modeling the evolution of hierarchical systems beyond MeSH. However, the significance is conditional on the validity of the independence assumptions underlying the error bars and on the reproducibility of the qualitative classification scheme, both of which need strengthening before the empirical claims can be fully trusted.

major comments (4)
  1. [Data and methods, Eqs. (2), (10); Supporting Information Table I] The binomial error model in Eq. (2) treats each attachment or deletion event as an independent Bernoulli trial with a fixed probability u(x), and Eq. (10) sums variances over years. However, MeSH updates are coordinated annual curation batches, not independent per-link decisions. Supporting Information Table I shows hierarchy G in 2008 undergoing 632 node deletions, 1059 link deletions, and 345 old-to-new link additions in a single year, and hierarchy N in 2008 adding 254 nodes and 244 new-to-new links. Such coordinated restructuring induces positive correlations among events, so the variance around W_rand is underestimated and the classification labels, especially w+ and w- but possibly some s+/s- cells dominated by one batch, may be false positives. The authors should test for overdispersion, use a year-clustered bootstrap, or repeat the analysis excluding the major restructuring years.
  2. [Results, category definitions] The distinction between 'strong' and 'weak' preference is not reproducible: the categories are defined by whether W_emp(x) exceeds W_rand(x) + sigma(W_rand(x)) by 'a large amount' or 'a small amount', with no numerical threshold. Table 2 and the aggregated Table 3 therefore depend on an unreported judgment call. A quantitative rule (for example, W_emp above W_rand + k sigma for a stated constant k, or a formal test statistic applied uniformly to all cells) is needed.
  3. [Tables 2, S8-S14, and Table 3] The analysis classifies on the order of hundreds of cells (7 hierarchies, 5 link-change types, and 8 property-by-endpoint combinations per hierarchy), yet no correction for multiple testing is applied. Under the null hypothesis, a substantial number of w+ and w- labels would be expected to appear by chance. The authors should report adjusted significance levels or quantify the expected number of false classifications.
  4. [Table 3 and aggregation method] The aggregated Table 3 averages labels with weights s+=1, w+=p+=0.5, s0=0, w-=p-=-0.5, s-=-1, irrespective of the number of events or the statistical power underlying each label. A strong label from a hierarchy with few events contributes the same weight as one from hierarchy D with many events, and cells with more than three i.s. entries are simply marked i.s., potentially hiding genuine signals in smaller hierarchies. Weighting by event counts or by a confidence measure would make the aggregation more defensible.
minor comments (5)
  1. [Abstract and throughout] The term 'MeSH' is misspelled as 'MesH' in several places, including the abstract and the introduction.
  2. [Data and methods, basic properties] The sentence 'the total number of descendants of the individual roots ... varies roughly between a 1,00 and a 10,000 nodes' contains a typo and should read 'between 100 and 10,000 nodes'.
  3. [Discussion] The phrase 'the likelihood for nodes to take part in restructuring events can be effected by their properties' should use 'affected' rather than 'effected'.
  4. [Tables 2 and 3] The column headers for the link-change types are difficult to parse because of repeated 'source:' and 'target:' lines; clearer labels such as 'add new->new', 'add new->old', 'add old->new', 'add old->old', and 'delete old->old' would improve readability.
  5. [Figure 3] The text refers to colors 'orange' and 'blue' for the curves; if the journal does not guarantee color printing, the figure should also use distinguishable line styles or markers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: preferences are measured against an empirical null baseline derived from the data, not fitted or defined in terms of the conclusions.

full rationale

The paper's central claims are empirical measurements rather than derivations from assumptions that already contain the conclusion. W_emp(x) in Eq. (8) is constructed from observed counts w_t(x) of link-change events, while the neutral baseline W_rand and its standard deviation in Eqs. (9)-(10) are computed from the complementary cumulative distribution Q_t(x) of the available nodes or links under the null hypothesis of uniform selection. No parameter is fitted to the event counts and then reported as a prediction; the preference and anti-preference classifications are direct comparisons between observed and null expectations. The only self-citation, Ref. [23] (with a duplicate as Ref. [47]), supplies the comparison method from Pollner et al. 2006; this is a general methodological tool rather than a result specific to MeSH, and it is independently validated by the paper's own simulations in Fig. 2. Concerns about the binomial independence assumption under curated batch updates, such as the large coordinated restructuring of hierarchy G in 2008, are about statistical validity and overdispersion, not circularity: a too-narrow error band could cause false positive classifications, but it does not make the measured W_emp equal to the null model or to any fitted input. No load-bearing step reduces to its own inputs by construction, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a statistical comparison between observed and expected link changes, with no fitted parameters and no new theoretical entities. The key assumptions concern data quality, event independence, the choice of null model, and the representativeness of the analyzed hierarchies.

assumptions (4)
  • domain assumption MeSH yearly snapshots provide an accurate and complete representation of the hierarchy evolution.
    All measurements are taken from the public MeSH files; undocumented bulk changes or curation errors propagate into event counts.
  • standard math Attachment and detachment events are independent Bernoulli trials with a fixed per-event probability u(x).
    Eq. (2) models w(x) as binomial; curator-driven batch changes may correlate events and invalidate the error bands.
  • domain assumption Uniform random choice of nodes for attachment and of links for detachment is the correct neutral baseline.
    The entire preference measure is defined relative to this baseline; a different null model could change the inferred preferences.
  • domain assumption Hierarchies with more than 1000 nodes are sufficient to generalize to all 16 MeSH hierarchies.
    Only hierarchies A, B, C, D, E, G, and N are analyzed; smaller hierarchies may behave differently.

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Cite this review

Pith. "Pith review of Time evolution of the hierarchical networks between PubMed MeSH terms." pith.science (2026). https://pith.science/paper/NMEN273P

@misc{pith2026190810214,
  author       = {Pith},
  title        = {Pith review of: Time evolution of the hierarchical networks between PubMed MeSH terms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NMEN273P}},
  note         = {Machine review of arXiv:1908.10214}
}
read the original abstract

Hierarchical organisation is a prevalent feature of many complex networks appearing in nature and society. A relating interesting, yet less studied question is how does a hierarchical network evolve over time? Here we take a data driven approach and examine the time evolution of the network between the Medical Subject Headings (MeSH) provided by the National Center for Biotechnology Information (NCBI, part of the U. S. National Library of Medicine). The network between the MeSH terms is organised into 16 different, yearly updated hierarchies such as "Anatomy", "Diseases", "Chemicals and Drugs", etc. The natural representation of these hierarchies is given by directed acyclic graphs, composed of links pointing from nodes higher in the hierarchy towards nodes in lower levels. Due to the yearly updates, the structure of these networks is subject to constant evolution: new MeSH terms can appear, terms becoming obsolete can be deleted or be merged with other terms, and also already existing parts of the network may be rewired. We examine various statistical properties of the time evolution, with a special focus on the attachment and detachment mechanisms of the links, and find a few general features that are characteristic for all MeSH hierarchies. According to the results, the hierarchies investigated display an interesting interplay between non-uniform preference with respect to multiple different topological and hierarchical properties.

Figures

Figures reproduced from arXiv: 1908.10214 by the authors.

Figure 1
Figure 1. Changes between subsequent time steps in a MeSH hierarchy a) A small part of the hierarchy ’A’ (Anatomy) in 2002. Red links are deleted in the next time step b) The corresponding part of the same hierarchy in 2003. Nodes and links colored red are newly appearing elements. as a function of x, whereas in the opposite case, when the attachment/detachment prefers lower values of x, the shape of W(x) becomes decreasing. … view at source ↗
Figure 2
Figure 2. Testing W(x) by simulated attachments. The property x here corresponds to the number of children, and the full symbols connected by continuous lines show the measured W(x) for random attachment (independent of x) in orange (circles), and for preferential attachment with an additive constant (i.e. when a newly added node connects to node i with a probability P ki+a i ki+a where a is an arbitrary constant) in blue (sq… view at source ↗
Figure 3
Figure 3. Measuring preference in attachment and detachment events. In each panel we compare Wemp(x) defined in (8) to the mean and standard deviation of W(x) for random events, given in (9-10) and indicated by dashed lines in shaded areas. The pictograms beside the panels show the type of the studied attachment/detachment events and highlight in red whether the given property x was measured on the source or on the target of … view at source ↗

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