Pith. sign in

REVIEW 3 major objections 4 minor 48 references

Missing links prediction: comparing machine learning with physics-rooted approaches

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that physics-rooted maximum-entropy models—using only coarse structural features like node degrees and geographic distances—predict missing links in economic and financial networks with accuracy comparable to, and in one c

desk verdict A careful benchmark showing max-entropy models can match a GBDT on missing-link recovery, with a real reproducibility gap and an overgeneralized missingness assumption. read the letter →

arxiv 2601.23061 v2 pith:USUFPSEX submitted 2026-01-30 physics.soc-ph physics.app-phphysics.data-an

Francesca Santucci , Giulio Cimini , Tiziano Squartini This is my paper · ORCID
classification physics.soc-phphysics.app-phphysics.data-an PACS 89.75.Fb02.50.Tt
keywords linkpredictionmaximum-entropymodelsConfigurationModelgradientboostingWorldTradeWebinterbanknetworksnetworkreconstructionwhite-boxvsblack-box
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 asks whether a black-box machine-learning model is actually necessary for predicting missing links in economic and financial networks. It compares the Gradient Boosting Decision Tree algorithm with physics-rooted maximum-entropy models—the Configuration Model and its fitness-based variants—on the World Trade Web and the electronic Market for Interbank Deposits. The central finding is that the white-box entropy models, which take as input only coarse quantities such as node degrees and distances, recover missing links with accuracy comparable to the GBDT, and the Configuration Model with Distances outperforms its GBDT counterpart on the trade network. If this holds, link prediction does not require fine-grained edge-level information; simple, interpretable, and fast models are viable competitors.

What carries the argument

The central object is the maximum-entropy random-graph ensemble, specifically the Configuration Model and its variants, which produce a probability p_ij for each non-observed pair by maximising entropy under constraints such as the observed degree sequence (and optionally total distances). These probabilities are used as ranking scores to select the |E_miss| most likely missing links. The comparison protocol—random deletion of a fixed share of links, averaging over ten realizations, and measuring TPR, JI, ACC, and AUROC—lets each white-box model be compared to a GBDT instance trained on exactly the same input features, isolating the contribution of the model family from the information fed t

What would settle it

Construct a controlled test in which missing links are removed by a systematic rule rather than at random—for instance, deleting all trade links below a volume threshold or all links incident to peripheral nodes—and measure whether the Configuration Model with Distances still matches or beats the gradient-boosting classifier; if its advantage disappears, the random-deletion assumption is the load-bearing premise.

Watch

Extended reading notes

Core claim

Running likelihood-based entropy benchmarks alongside a gradient-boosting classifier under the same training protocol, the authors find that the Configuration Model—which assigns each pair of nodes a connection probability from the observed degree sequence—matches the GBDT when both are fed the same 'endogenous' features, and that enriching the Configuration Model with geographic distances (CMD) yields higher TPR, JI, and AUROC than the GBDT on the World Trade Web. On the interbank market, each endogenous GBDT instance performs comparably to the purely structural white-box models. The paper interprets this as evidence that topological information is decisive in shaping network topology and t

Load-bearing premise

The benchmark's validity rests on the assumption that a model's accuracy on the observed portion of a network transfers to the missing portion—that is, the hidden links are missing at random and behave like the visible ones.

Editorial extensions

If this is right

  • The Configuration Model alone, using only node degrees, can reach the accuracy of a gradient-boosting classifier trained on the same degree features, so structural information can do much of the work.
  • Adding a single exogenous quantity (geographic distance) to the Configuration Model produces a white-box model that outperforms the corresponding GBDT on the World Trade Web.
  • Because white-box models need only aggregated quantities (degrees, total links) rather than the exact pattern of observed edges, they can be applied when fine-grained edge-level information is unavailable or unreliable.
  • The paper's results suggest that the machine-learning advantage over simple models in link prediction is not general; it depends on the features and the training protocol.
  • White-box reconstruction-style models generalize more robustly across datasets, while the GBDT performs poorly or cannot run when trained on one network to predict another.

Reading between the lines

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

  • A natural next test is to delete links in a biased way—e.g., removing all trade links below a volume threshold or all links incident to peripheral nodes—to see whether the white-box models' standing changes; real-world missingness in trade and financial data may not be random.
  • The success of the Configuration Model with Distances suggests that explicitly encoding spatial costs into entropy benchmarks could be a general principle for other geographic or transportation networks.
  • The comparable accuracy of the single-constraint CM to the fit2SM indicates that, for these dense economic networks, higher-order degree-correlation information adds little; testing on sparser networks would reveal where non-linear models start to matter.
  • The protocol compares models under equal information, but a practical comparison would also account for the cost of acquiring input features, which would likely strengthen the case for white-box models.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper compares two families of link-prediction algorithms on binary, undirected representations of the World Trade Web (WTW, 1990–2000) and the electronic Market for Interbank Deposits (eMID, 1999–2014). The physics-rooted family includes the Gravity Model, Configuration Model, Chung-Lu model, fitness models, fitness models with distances, and a fitness-induced 2-star model; the machine-learning family is a Gradient Boosting Decision Tree implemented with LightGBM. The protocol randomly deletes 10–50% of links (10 replicates), trains on the remaining graph, and evaluates TPR, JI, ACC, and AUROC. The central claim is that likelihood/entropy-based models—especially the Configuration Model and its distance-augmented variant—achieve accuracy comparable to, and sometimes slightly higher than, the GBDT when given the same input information, and that white-box models are therefore viable competitors that are more interpretable and computationally faster.

Significance. If the central claim holds, the paper provides a useful benchmark result for economic and financial networks: a simple, interpretable maximum-entropy model can match a state-of-the-art gradient-boosting classifier in link prediction when both use the same coarse inputs. The strength of the paper is its careful specification of the iterative recipes for the maximum-entropy models (Eqs. 28, 32, 35, 38, 45), the use of multiple metrics and deletion fractions, and the additional robustness checks in Appendices A–C, including a different train/test split protocol. These elements make the comparison reproducible in principle. However, the general conclusion is currently supported only under a missing-completely-at-random protocol, and the ML baseline is not fully specified, so the scope of the claim needs tightening.

major comments (3)
  1. [§III.C, footnote 1; §II] The benchmark deletes edges uniformly at random (10–50%, repeated 10 times), and the paper's own premise (footnote 1, §III.C) is that a model reproducing the observed portion will reproduce the missing portion with the same accuracy. This exchangeability assumption is not tested. In both empirical settings, real missingness is plausibly non-MCAR: WTW links are derived from reported trade volumes (missingness concentrated among small/under-reporting economies), and eMID has a €50,000 reporting threshold and an Italian-bank subgraph. Under biased missingness, the observed degree sequence k_i(A_obs), the core input of CM/CMD/fit2SM, is a systematically biased estimate of the true degrees, and the ranking of white-box models against the GBDT could change. The abstract's general claim that white-box algorithms are 'viable competitors' is therefore only established for random deletion. Please
  2. [§III.B; Abstract] The GBDT implementation is described only as 'LightGBM' (ref. [26]); no hyperparameters, tuning procedure, or validation strategy are reported. Since the paper's conclusion is that white-box models perform comparably to this specific GBDT instance, the absence of the hyperparameter configuration makes the baseline unverifiable and potentially unrepresentative. In addition, the abstract and Discussion claim that white-box models are 'computationally faster' than the GBDT, but no runtime measurements or complexity comparison are provided anywhere in the manuscript. Please either report the LightGBM configuration and a runtime table, or remove/qualify the speed claim.
  3. [§IV, Figs. 2–6; Appendix A] The central comparative claims—'comparable', 'slightly higher', 'outperforms'—are based on averages over 10 random link deletions, with standard deviations shown as error bars. No statistical significance tests are reported for any metric or dataset. Given that the bar overlaps are substantial in several panels (e.g., Fig. 2, TPR panels for CMD vs GBDT; Fig. 6, eMID AUROC), the claimed differences could be within sampling noise. Please add paired tests across the 10 realizations (e.g., Wilcoxon signed-rank tests) or otherwise demonstrate that the observed differences are not due to chance, and adjust the wording where significance is lacking.
minor comments (4)
  1. [Overall structure] The section numbering is duplicated: 'III. MISSING LINKS PREDICTION' is followed by another 'III. DATA DESCRIPTION'. The subsequent sections should be renumbered.
  2. [§III (Data Description), eMID binarisation] The expression for symmetrisation reads 'a_ij = Θ[w_ij + w_ij]'; this should presumably be Θ[w_ij + w_ji].
  3. [Eq. (10)] The notation assigns α = ln ε but uses ε inside the logarithm; the definition of ε is implicit. Please clarify whether α is a fitted constant or derived from ε.
  4. [Appendix B] The eMID daily snapshots have average degree as low as 4.61, yet the same 20% deletion fraction is used for all aggregation levels. A brief justification of why 20% is appropriate at daily scale, or a sensitivity check, would strengthen the appendix.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the comparison is a held-out external benchmark against GBDT ground truth; self-citations are contextual and non-load-bearing.

full rationale

The derivation chain is self-contained: every physics-rooted model is fully specified in the paper (eqs. 26-45), with parameters fitted by moment-matching on the observed portion A_obs (degrees, total links, two-stars, total distance), while the reported accuracy (TPR, JI, ACC, AUROC) is computed on the held-out deleted links E_miss against ground truth that never enters the fitting. No fitted quantity is renamed as a prediction: matching the observed degree sequence, L, S, or d by construction says nothing about which specific non-observed pairs are the missing ones, so the ranking vs. the GBDT is an external benchmark. The GBDT is an independent implementation (LightGBM) trained on the same observed labels, with the true labels of E_miss withheld. Self-citations — [6] for the deletion framework, [39] for the eMID data and the dc2SM caveat, [37] for iterative recipes, [1,9,31,33,40,45] for context — are not load-bearing: the central comparison rests on the paper's own experiments. The dc2SM limitation attributed to [39] justifies a modeling choice but does not determine the CM/FMD/CMD results, which are defined and fitted in this paper itself. No uniqueness theorem is imported to force a choice, and no ansatz is smuggled via citation: the Boltzmann-logistic forms of eqs. 21-24 and the CM/FM equations are standard and stated. Flagged limitation (footnote 1, §III.C): the paper asserts, rather than proves, that accuracy on the observed portion transfers to the missing portion; the random-deletion (MCAR) protocol makes the benchmark internally as fair as possible, but real trade/financial missingness (reporting thresholds, small economies) may be non-MCAR. That is an external-validity/correctness risk, not a circular step. Score 2 reflects only the presence of several minor, non-load-bearing self-citations; there is no constructional circularity.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central comparison depends on standard maximum-entropy model equations, an explicit missing-at-random/stationarity assumption, and several fitted parameter sets (GM alpha-beta-gamma, CM x_i, CMD x_i/w, FM z, FMD z/w, fit2SM z/y). No new entities are introduced. The ledger is dominated by model parameters fitted to the observed portion—standard supervised fitting rather than hidden assumptions—plus the stated assumption that accuracy on the observed portion transfers to the missing portion.

free parameters (7)
  • GM coefficients alpha, beta, gamma = Per year, e.g. 1990: alpha=2.102±0.020, beta=0.436±0.004, gamma=0.526±0.009 (Table I)
    Fitted by maximum likelihood on observed links (eqs. 11-14); define the GM-II scores used in the comparison.
  • CM node parameters x_i = not reported
    Fitted via iterative fixed point (eqs. 27-28) to reproduce observed degrees; core of CM probabilities in eq. 26.
  • CMD node parameters x_i and distance parameter w = not reported
    Fitted via eqs. 31-32; needed for CMD scores, the best-performing white-box model on WTW.
  • FM scale parameter z = not reported
    Fitted via eqs. 34-35 to match observed link density; defines FM probabilities in eq. 33.
  • FMD scale parameter z and distance parameter w = not reported
    Fitted via eqs. 37-38; used for FMD scores.
  • fit2SM parameters z and y = not reported
    Fitted via iterative recipe eqs. 44-45, with x_i taken from the CM; used for fit2SM scores.
  • GBDT hyperparameters = not reported
    LightGBM hyperparameters (learning rate, number of trees, max depth, etc.) are not specified in §III.B; they affect the GBDT accuracy that the white-box models are compared against.
assumptions (7)
  • standard math Maximum-entropy ensemble: P(G|theta)=e^{-C(G)·theta}/Z(theta); likelihood maximization is equivalent to <C>=C(G*)
    Used to define CM/CMD/FM/FMD/fit2SM probabilities (eqs. 21-24); standard ERG result, not proved in the paper.
  • standard math Iterative fixed-point recipes (eqs. 28, 32, 35, 38, 45) converge to the unique solution of the constraint equations
    Assumed without proof; standard for these models.
  • domain assumption Links missing from the network are missing at random
    Simulated by deleting 10-50% of links uniformly at random (§II); real missingness may be systematic.
  • domain assumption Accuracy on the observed portion transfers to the missing portion
    Explicit statement in footnote 1 after eq. (28): 'if the accessible portion ... reproduced with a certain accuracy ... inaccessible portion will be reproduced with the same degree of accuracy.' This is the load-bearing stationarity premise.
  • domain assumption Exogenous features (GDP, distance) are available and reliable for all test pairs; eMID lacks such features, so only endogenous comparisons are made there
    Needed for GM/FM/FMD/CMD feature inputs (§III, §IV).
  • domain assumption Binarization and symmetrization a_ij=Theta[w_ij] (WTW) and a_ij=Theta[w_ij+w_ji] (eMID) preserve predictive signal
    Data preprocessing in §III; affects all degree/strength features and all results.
  • ad hoc to paper The GBDT baseline with unstated LightGBM hyperparameters is representative of machine-learning link predictors
    No hyperparameter values or tuning procedure are given in §III.B; the comparison treats this single configuration as 'the' ML approach.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Missing links prediction: comparing machine learning with physics-rooted approaches." pith.science (2026). https://pith.science/paper/USUFPSEX

@misc{pith2026260123061,
  author       = {Pith},
  title        = {Pith review of: Missing links prediction: comparing machine learning with physics-rooted approaches},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/USUFPSEX}},
  note         = {Machine review of arXiv:2601.23061}
}
read the original abstract

An active research line within the broader field of network science is the one concerning link prediction. Close in scope to network reconstruction, link prediction targets specific connections with the aim of uncovering the missing ones, as well as predicting those most likely to emerge in the future, from the available information. In this paper, we consider two families of methods, i.e. those rooted in statistical physics and those based upon machine learning: the members of the first family identify missing links as the most probable non-observed ones, the probability coefficients being determined by solving maximum-entropy benchmarks over the accessible network structure; the members of the second family, instead, associate the presence of single edges to explanatory node-specific variables. Running likelihood-based models such as the Configuration Model, or one of its many fitness-based variants, in parallel with the Gradient Boosting Decision Tree algorithm reveals that the accuracy of the former is comparable to the accuracy of the latter. Such a result confirms that white-box algorithms are viable competitors to the currently available black-box ones, being more interpretable and computationally faster.

Figures

Figures reproduced from arXiv: 2601.23061 by the authors.

Figure 1
Figure 1. Visual representation of the framework adopted to carry out link prediction in [ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Performance of the models, measured in terms of TPR, for the years 1990, 1995 and 2000 of the WTW. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Performance of the models, measured in terms of JI, for the years 1990, 1995 and 2000 of the WTW. Each [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Performance of the models, measured in terms of ACC, for the years 1990, 1995 and 2000 of the WTW. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Panels a: performance of the models, measured in terms of ROC curves, for the years 1990, 1995 and 2000 of the WTW. Each panel collects methods that rely on the same set of features. We have randomly selected the 10% of links 10 times to populate E miss and generate E …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 3 canonical work pages

  1. [26]

    Pedregosa, G

    F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cour- napeau, M. Brucher, M. Perrot, and\. Duchesnay, Jour- nal of Machine Learning Research12, 2825 (2011)

    2011

  2. [1]

    Link prediction via linear ERGs Configuration Model.Let us, now, consider the first spec- ification of the entropy-based framework: it boils down to posingC=k, withk i = P j(̸=i) aij, an identifica- tion that leads toH CM(A) = PN i=1 P j(>i) aij ·(θ i +θ j), further inducing pCM ij = xixj 1 +x ixj ,(26) wherex i =e −θi ; the parameters{x i}N i=1 can be de...

  3. [2]

    Link prediction via non-linear ERGs So far, we have focused on linear ERGs; let us, now, move to considering non-linear ERGs. Fitness-induced 2-Star Model.The simplest model of this kind is the so-called2-Star Model(2SM) [27, 46, 47], induced by posingC={L, S}, with 7 L= PN i=1 P j(>i) aij = PN i=1 ki/2 andS= PN i=1 P j(>i) P m(̸=i,j) aimamj = PN i=1 k2 i...

    1990

  4. [3]

    Squartini, G

    T. Squartini, G. Caldarelli, G. Cimini, A. Gabrielli, and D. Garlaschelli, Physics Reports Reconstruction methods for networks: The case of economic and financial systems, 757, 1 (2018)

    2018

  5. [4]

    L¨ u and T

    L. L¨ u and T. Zhou, Physica A: Statistical Mechanics and its Applications390, 1150 (2011)

    2011

  6. [5]

    Liben-Nowell and J

    D. Liben-Nowell and J. Kleinberg, Journal of the American Society for Information Sci- ence and Technology58, 1019 (2007), eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/asi.20591

    doi:10.1002/asi.20591 2007

  7. [6]

    Berlusconi, F

    G. Berlusconi, F. Calderoni, N. Parolini, M. Verani, and C. Piccardi, PLOS ONE11, e0154244 (2016), publisher: Public Library of Science

    2016

  8. [7]

    Jalili, Y

    M. Jalili, Y. Orouskhani, M. Asgari, N. Alipourfard, and M. Perc, Royal Society Open Science4, 160863 (2017), publisher: Royal Society

    2017

Show all 48 references
  1. [8]

    Parisi, G

    F. Parisi, G. Caldarelli, and T. Squartini, Applied Net- work Science3, 10.1007/s41109-018-0073-4 (2018), pub- lisher: Springer Science and Business Media Deutschland GmbH

    2018 doi

  2. [9]

    Mungo, F

    L. Mungo, F. Lafond, P. Astudillo-Est´ evez, and J. D. Farmer, Journal of Economic Dynamics and Control148, 104607 (2023). 15

    2023

  3. [10]

    Bardoscia, P

    M. Bardoscia, P. Barucca, S. Battiston, F. Caccioli, G. Cimini, D. Garlaschelli, F. Saracco, T. Squartini, and G. Caldarelli, Nature Reviews Physics3, 490 (2021), pub- lisher: Nature Publishing Group

    2021

  4. [11]

    L. N. Ialongo, C. de Valk, E. Marchese, F. Jansen, H. Zmarrou, T. Squartini, and D. Garlaschelli, Scientific Reports12, 11847 (2022), publisher: Nature Publishing Group

    2022

  5. [12]

    A. L. Barab´ asi and R. Albert, Science286, 509 (1999)

    1999

  6. [13]

    T. Zhou, L. L¨ u, and Y.-C. Zhang, The European Physical Journal B71, 623 (2009)

    2009

  7. [14]

    Katz, Psychometrika18, 39 (1953)

    L. Katz, Psychometrika18, 39 (1953)

    1953

  8. [15]

    Brin and L

    S. Brin and L. Page, Computer Networks and ISDN Systems Proceedings of the Seventh International World Wide Web Conference,30, 107 (1998)

    1998

  9. [16]

    P. Y. Chebotarev and E. Shamis, The Matrix-Forest The- orem and Measuring Relations in Small Social Groups (1997)

    1997

  10. [17]

    Jeh and J

    G. Jeh and J. Widom, SimRank: A Measure of Structural-Context Similarity (2002)

    2002

  11. [18]

    Liu and L

    W. Liu and L. L¨ u, Europhysics Letters89, 58007 (2010)

    2010

  12. [19]

    Clauset, C

    A. Clauset, C. Moore, and M. E. J. Newman, Nature 453, 98 (2008), publisher: Nature Publishing Group

    2008

  13. [20]

    Guimer` a and M

    R. Guimer` a and M. Sales-Pardo, Proceedings of the Na- tional Academy of Sciences of the United States of Amer- ica106, 22073 (2009)

    2009

  14. [21]

    Adriaens, A

    F. Adriaens, A. Mara, J. Lijffijt, and T. De Bie, inPro- ceedings - 2020 IEEE 7th International Conference on Data Science and Advanced Analytics, DSAA 2020(In- stitute of Electrical and Electronics Engineers Inc., 2020) pp. 70–80

    2020

  15. [22]

    Friedman, L

    N. Friedman, L. Getoor, D. Koller, and A. Pfeffer, inIJ- CAI International Joint Conference on Artificial Intelli- gence, Vol. 2 (International Joint Conferences on Artifi- cial Intelligence, 1999) pp. 1300–1307, iSSN: 1045-0823

    1999

  16. [23]

    K. Yu, W. Chu, S. Yu, V. Tresp, and Z. Xu, inAdvances in Neural Information Processing Systems, Vol. 19 (MIT Press, 2006)

    2006

  17. [24]

    Isard, The Quarterly Journal of Economics68, 305 (1954)

    W. Isard, The Quarterly Journal of Economics68, 305 (1954)

    1954

  18. [25]

    Tinbergen,Shaping the World Economy; Suggestions for an International Economic Policy(1962)

    J. Tinbergen,Shaping the World Economy; Suggestions for an International Economic Policy(1962)

    1962

  19. [27]

    J. H. Friedman,Greedy function approximation: a gradi- ent boosting machine, Tech. Rep. 5 (The Annals of Statis- tics, 2001) publication Title: The Annals of Statistics Volume: 29

    2001

  20. [28]

    G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye, and T.-Y. Liu, inAdvances in neural information processing systems, Vol. 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vish- wanathan, and R. Garnett (Curran Associates, Inc., 2017)

    2017

  21. [29]

    Park and M

    J. Park and M. E. J. Newman, Physical Review E70, 066117 (2004), publisher: American Physical Society

    2004

  22. [30]

    Bianconi, Europhysics Letters81, 28005 (2007)

    G. Bianconi, Europhysics Letters81, 28005 (2007)

    2007

  23. [31]

    Squartini and D

    T. Squartini and D. Garlaschelli, New Journal of Physics 13, 10.1088/1367-2630/13/8/083001 (2011)

    2011 doi

  24. [33]

    Squartini, R

    T. Squartini, R. Mastrandrea, and D. Garlaschelli, New Journal of Physics17, 023052 (2015), publisher: IOP Publishing

    2015

  25. [34]

    Saracco, R

    F. Saracco, R. Di Clemente, A. Gabrielli, and T. Squar- tini, Scientific Reports5, 10595 (2015), publisher: Nature Publishing Group

    2015

  26. [35]

    Cimini, T

    G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, and G. Caldarelli, Nature Reviews Physics 1, 58 (2019), publisher: Nature Publishing Group

    2019

  27. [36]

    S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Nucl. Phys. B666, 396 (2003), eprint: cond- mat/0204111

    2003

  28. [37]

    Park and M

    J. Park and M. E. J. Newman, Physical Review E68, 026112 (2003), publisher: American Physical Society

    2003

  29. [38]

    Garlaschelli and M

    D. Garlaschelli and M. I. Loffredo, Physical Review E78, 015101 (2008), publisher: American Physical Society

    2008

  30. [39]

    Vallarano, M

    N. Vallarano, M. Bruno, E. Marchese, G. Trapani, F. Saracco, G. Cimini, M. Zanon, and T. Squartini, Sci- entific Reports11, 10.1038/s41598-021-93830-4 (2021)

    2021 doi

  31. [41]

    Marzi, F

    M. Marzi, F. Giuffrida, D. Garlaschelli, and T. Squartini, Reproducing the first and second moment of empirical degree distributions (2025), arXiv:2505.10373 [physics]

    2025 arXiv

  32. [42]

    Cimini, R

    G. Cimini, R. Mastrandrea, and T. Squartini,Recon- structing Networks(Cambridge University Press, 2021) google-Books-ID: 3U0 EAAAQBAJ

    2021

  33. [43]

    Picciolo, T

    F. Picciolo, T. Squartini, F. Ruzzenenti, R. Basosi, and D. Garlaschelli, in2012 Eighth International Conference on Signal Image Technology and Internet Based Systems (2012) pp. 784–792

    2012

  34. [44]

    Bianconi, Information theory of spatial network en- sembles (2022), arXiv:2206.05614 [cond-mat]

    G. Bianconi, Information theory of spatial network en- sembles (2022), arXiv:2206.05614 [cond-mat]

    2022 arXiv

  35. [45]

    Caldarelli, A

    G. Caldarelli, A. Capocci, P. De Los Rios, and M. A. Mu˜ noz, Physical Review Letters89, 10.1103/Phys- RevLett.89.258702 (2002)

    2002 doi

  36. [46]

    Garlaschelli and M

    D. Garlaschelli and M. I. Loffredo, Physical Review Let- ters93, 10.1103/PhysRevLett.93.188701 (2004), pub- lisher: American Physical Society

    2004 doi

  37. [47]

    Cimini, T

    G. Cimini, T. Squartini, D. Garlaschelli, and A. Gabrielli, Scientific Reports5, 15758 (2015), publisher: Nature Publishing Group

    2015

  38. [48]

    Park and M

    J. Park and M. E. J. Newman, Physical Review E70, 066146 (2004), publisher: American Physical Society

    2004

  39. [49]

    Bolfe, F

    M. Bolfe, F. L. Metz, E. Guzm´ an-Gonz´ alez, and I. P. Castillo, Physical Review E104, 014147 (2021), arXiv:2102.09629 [cond-mat]

    2021 arXiv

  40. [50]

    K. S. Gleditsch, Journal of Conflict Resolution46, 712 (2002), publisher: Peace Science Society (International). 16 1990 1995 2000 year 0.80 0.85 0.90 0.95AUROC 1990 1995 2000 year 0.75 0.80 0.85 0.90 0.95ACC 1990 1995 2000 year 0.3 0.4 0.5 0.6 0.7 0.8JI 1990 1995 2000 year 0....

    2002

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.