Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Patent collaboration networks hide a role-based, core-periphery architecture that standard community detection misses, and this architecture is where citation impact concentrates.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-03 10:20 UTC pith:WICOQ2IP

load-bearing objection A decent descriptive study of six new patent collaboration networks with a welcome code release, but the inequality results rest on an unspecified patent-to-cluster attribution rule that likely double-counts citations, so the strong conclusions need fixing before they can stand. the 3 major comments →

arxiv 2601.10224 v3 pith:WICOQ2IP submitted 2026-01-15 econ.GN physics.soc-phq-fin.EC

The hidden structure of innovation networks

Lorenzo Emer , Anna Gallo , Mattia Marzi , Andrea Mina , Tiziano Squartini , Andrea Vandin This is my paper
classification econ.GN physics.soc-phq-fin.EC PACS 89.75.Fb02.50.Tt
keywords innovation networksco-inventorshipco-ownershipstochastic block modelBayesian information criterionmodularity maximizationforward citationsLorenz curve
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper studies how inventive activity organizes at the mesoscale by building co-inventorship and co-ownership networks among the top-500 cited actors in artificial intelligence, biotechnology, and semiconductors. It compares modularity maximization, a standard community-detection baseline, against inference-based Stochastic Block Models selected by the Bayesian Information Criterion. The paper's central claim is that modularity alone cannot see the real architecture: the inference method exposes tree-like, role-based organizations with locally core-periphery structures, and these structures align with inequality in forward citations. A sympathetic reader should care because the choice of detection method changes which actors appear to hold influence, and therefore which collaborations look like suitable targets for policy.

Core claim

On the paper's own terms, the discovery is a three-part structural finding. First, inventor networks are denser, more clustered, and more homogeneous than organization networks, suggesting recurrent small teams embedded in institutional hierarchies. Second, when clusters are inferred by minimizing BIC under the SBM and its degree-corrected variant, organization networks display a clearer role-based, core-periphery architecture—few bridging firms coordinate peripheral actors—whereas modularity partitions fragment the network into smaller, denser communities. Third, Lorenz curves of forward citations show that impact is strongly concentrated in a few clusters, and the concentration is sharper

What carries the argument

The load-bearing tool is the inference-based stochastic block model, fit by minimizing the Bayesian Information Criterion (BIC), together with its degree-corrected variant. The SBM treats block membership as a generative model and model selection as the balance between fit and complexity; the degree-corrected version adds per-node degree multipliers, letting hubs and peripheral nodes occupy the same block. This machinery is what converts community detection into role-based structure detection, uncovering core-periphery and tree-like patterns that modularity—which only rewards dense assortative groups—cannot represent. Lorenz curves of forward citations, computed per cluster, then link those

Load-bearing premise

The paper's inequality results assume that adding a patent's citations to every cluster it touches preserves the ranking; because such patents are counted in full for each cluster, the cumulative share of total citations is not a fixed total and can be inflated by overlap.

What would settle it

Assign each patent's forward citations to a single cluster—for example by legal owner, or by uniformly splitting among co-owners—and recompute the Lorenz curves; if the BIC-versus-modularity differences or the sector rankings disappear, the inequality claim rests on the over-counting of overlapping patents.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Standard modularity partitions split networks into smaller, more homogeneous clusters, flattening Lorenz curves and dispersing high-impact patents across groups; BIC-SBM and dcSBM yield steeper curves showing impact concentrated in cohesive cores.
  • Inventor-level collaboration networks consistently show higher citation-concentration inequality than organization-level networks across all three sectors.
  • Among organization networks, AI shows the strongest concentration of forward citations, while biotechnology and semiconductors are more balanced.
  • Organization nodes form local core-periphery structures with few bridging firms coordinating peripheral actors, whereas inventor clusters are dense, cross-firm, and technologically generalist.
  • Because the detected mesoscale structure differs by algorithm, downstream analyses of innovation ecosystems are method-sensitive: modularity-based maps would understate the role of hierarchical hubs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: If the causal reading holds, the bridging firms at the core of BIC-dcSBM blocks are structural bottlenecks; policies aimed at those nodes would have a proportionally larger effect on knowledge diffusion, whereas modularity-based targeting would miss them.
  • Editorial inference: A direct test of the paper's claim is to compare the out-of-sample predictive power of modularity versus BIC partitions for future citations; if role-based blocks genuinely channel impact, they should beat modularity communities as predictors.
  • Editorial inference: The cluster-level Lorenz-curve construction may double-count citations for patents touching several clusters; recomputing inequality with each patent assigned to exactly one block would disambiguate whether the finding is about overlap or concentration.
  • Editorial inference: Applying the same BIC-SBM pipeline to temporal snapshots could reveal whether cores precede or follow citation bursts, separating preferential attachment from role-based coordination.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies mesoscale structures in six patent collaboration networks (co-inventorship and co-ownership) in AI, biotechnology, and semiconductors, built from the top-500 actors ranked by forward citations. It compares modularity maximization with BIC-based Stochastic Block Model (SBM) and degree-corrected SBM (dcSBM) partitions, and relates the detected clusters to the distribution of forward citations via Lorenz curves and Gini coefficients. The authors report three main findings: inventor networks are denser and more clustered than organization networks; BIC-based inference recovers hierarchical/role-based structures that modularity misses; and citation impact is highly unequal across clusters, with algorithm-dependent differences in measured concentration.

Significance. If the central claims hold, the paper makes a useful contribution by bringing statistically grounded block-model inference into the empirical study of innovation networks and by showing that the choice of mesoscale detection method can affect conclusions about how collaboration structures channel inventive impact. The manuscript is generally clearly written, and the authors provide a downloadable Python package (DOMINO), explicit algorithmic pseudocode, and robustness checks on top-300 and top-700 networks. These are genuine strengths. However, the third main result — that BIC-based partitions reveal different citation concentration than modularity — rests on an ambiguous attribution of patents to clusters, and the quantitative comparisons lack uncertainty quantification. As it stands, the evidence for the headline inequality claim is not yet established.

major comments (3)
  1. [Section II C and Methods D, Eq. (10)] The definition of f_c^(r) in Eq. (10) is ambiguous in a way that is load-bearing for the Lorenz-curve and Gini results. Clusters partition nodes (inventors or organizations), not patents. A patent with inventors or owners in several clusters has no unique 'associated cluster'. If the implementation counts a patent's citations in every cluster containing any of its actors, then the same forward citations enter multiple cluster totals, the denominator in Eq. (10) is not the total citation pool, and the Lorenz curve is not a partition-based concentration measure. This could directly manufacture or mask algorithm-dependent differences in Fig. 7 and Table VII. The paper must specify a unique association rule (e.g., primary inventor/owner, fractional assignment, or node-level citation aggregation) and recompute the inequality results under that rule. The reported Gini differences — e.g., BT Or
  2. [Fig. 7 and Table VII] The algorithm-comparison claims about inequality are made without any uncertainty quantification or null model. The Gini coefficients differ substantially across algorithms in some sectors (e.g., SC Organizations: 0.570 for modularity vs. 0.278 for BIC-dcSBM), but no confidence intervals, bootstrap resampling, or permutation tests are reported. Because the partitions come from different objective functions and the citation attribution is ambiguous, the differences could be within noise. At minimum, provide bootstrap CIs for the Gini coefficients and Lorenz curves, and a null model that randomly assigns patents to clusters while preserving cluster sizes, to show that the algorithm-dependent ordering is not an artifact of the detection method.
  3. [Appendix C, Eqs. (B21)–(B22)] The dcSBM optimization is approximate: node-specific degree parameters are fixed from the UBCM before running Leiden, and a final joint fit is used only to compute the BIC value of the selected partition, not to refine the partition itself. The manuscript should state explicitly that the reported BIC-dcSBM partitions are not necessarily optima of the dcSBM objective, and should quantify the sensitivity of the resulting partitions to this approximation — for example, by comparing against an exact dcSBM fit on smaller networks or by checking whether the final joint fit changes the partition when re-applied. Without this, the paper's claim that dcSBM 'reconciles' the SBM and modularity pictures is not fully supported.
minor comments (4)
  1. [Appendix B, around Eq. (B11)] Typo: the equation for p_rr writes '2L_rs(A)/N_r(N_r-1)' but the within-block number of links should be L_rr.
  2. [Appendix B, near Eq. (B19)] The expression 'x_i x_j x_rs / (1 + x_i x_j x_rs)' appears to mix the block-affinity symbol and the degree-correction parameter; it should read 'x_i x_j χ_rs / (1 + x_i x_j χ_rs)'.
  3. [Section V.A] The choice of the top-500 most-cited actors is described as 'standard' but is also a selection on the outcome variable used later in the Lorenz-curve analysis. The limitations paragraph acknowledges the truncation, but it would help to state explicitly in the main text that all reported citation-concentration results are conditional on this selected sample.
  4. [Table VII caption] The Gini coefficients are reported to three decimal places without any measure of dispersion. Consider reporting the number of clusters used in each computation, since Gini estimates from few clusters can be sensitive to cluster-count differences across algorithms.

Circularity Check

0 steps flagged

No equation in the derivation chain reduces to its input; the modularity-vs-BIC comparison is an empirical comparison of partitions. Minor self-citations are not load-bearing.

full rationale

Walking the derivation chain: the BIC-SBM and BIC-dcSBM likelihoods are derived in Appendix B from an ERG maximum-entropy argument; no fitted parameter is later renamed as a prediction. The comparison between modularity maximization and BIC minimization is a comparison of partitions produced by two different objective functions on the same networks, and the structural metrics (IC/EC, within-cluster degree standard deviation, Lorenz curves) are computed after the partition is fixed. The Lorenz curve (Eqs. 9-11) is a direct transformation of citation totals assigned to clusters, not a fit; the statement that different algorithms yield different curves is an empirical fact about those partitions, not an identity. Self-citations (refs. 27, 32, 63, 64) support standard methodology (ERG derivation, Nakamoto index, similarity indices) and the required derivations are reproduced in the appendix, so no result is imported solely by the authors' authority. The main validity concern is the undefined association rule in Eq. (10): a patent with inventors or owners in multiple clusters may be counted in multiple f_c^(r), making the denominator of Eq. (10) not a fixed citation total. That is a measurement-validity problem for the Gini comparisons, not a circular reduction: no equation defining f_c^(r) is equivalent to the paper's conclusions by construction. Hence no significant circularity; the score of 2 reflects only the minor, non-load-bearing self-citations.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central claims do not introduce new physical entities, but they rely on several fitted parameters (block assignments, degree-correction coefficients, affinities, cutoffs) and modeling assumptions. The most fragile assumption is that citation impact can be attributed additively across clusters and that BIC-based block models are a privileged lens for 'hidden' hierarchy.

free parameters (5)
  • Number of nodes N (top-500 cutoff) = 500 (robustness: 300, 700)
    The authors select the 500 most-cited actors in each sector; this hand-chosen threshold directly shapes degree distributions, clustering, and citation-concentration measures (Section V.A).
  • Block counts K and block assignments = e.g., K=9–23 depending on network/algorithm
    K and node-to-block assignments are fit by BIC/Leiden; they define all mesoscale claims and the Lorenz-curve units (Section II.B).
  • Degree-correction parameters x_i (UBCM) = not reported numerically
    Node-level degree multipliers in the dcSBM are solved from observed degrees (Eq. B21, Appendix C); they are fitted to the data and kept fixed during the Leiden search.
  • Block affinity parameters χ_rs = not reported numerically
    Between/within-block connection propensities are fitted by maximum likelihood under the approximate dcSBM (Eq. B22); they determine which hierarchical structures are claimed.
  • IPC-entropy median cutoff = median of cluster entropies
    Used to split specialized vs generalist modules in Fig. 4; chosen post hoc to label quadrants.
axioms (6)
  • standard math BIC is a valid model-selection criterion for comparing network partitions
    The whole mesoscale comparison rests on BIC (Methods II.C.2), which is an asymptotic approximation; no ground-truth validation is provided.
  • domain assumption SBM/dcSBM generative models adequately describe inventor/ownership networks
    The claim that inferred blocks represent real hierarchy assumes the model family contains the true generating process (Eqs. 5–7).
  • domain assumption Forward citations measure technological impact
    Top-500 ranking and inequality analysis use forward citations as impact (ref [17]), a standard but contested assumption.
  • ad hoc to paper A patent's citations are additively attributable to every cluster containing any of its actors
    Eq. (10) defines f_c(r) as citations of all patents associated with cluster r; because a patent can be associated with multiple clusters, citation mass is double-counted and Lorenz curves are not a partition of a fixed total.
  • domain assumption The top-500 most-cited actors are a representative window on innovation networks
    Robustness at 300/700 tests size, not representativeness; all thresholds select on the outcome (Section V.A).
  • domain assumption Static, five-year aggregation captures mesoscale architecture
    Networks are aggregated 2020–2024 and treated as static; temporal dynamics are acknowledged as a limitation in Section IV.

pith-pipeline@v1.3.0-alltime-deepseek · 98 in / 12421 out tokens · 194398 ms · 2026-08-03T10:20:31.326230+00:00 · methodology

0 comments
read the original abstract

Innovation emerges from complex collaboration patterns - among inventors, firms, or institutions. However, not much is known about the overall mesoscopic structure around which inventive activity self-organizes. Here, we tackle this problem by employing patent data to analyze both individual (\textit{co-inventorship}) and organization (\textit{co-ownership}) networks in three strategic domains (\textit{artificial intelligence}, \textit{biotechnology} and \textit{semiconductors}). We characterize the mesoscale structure (in terms of clusters) of each domain by comparing two alternative methods: a standard baseline - modularity maximization - and one based on the minimization of the Bayesian Information Criterion, within the Stochastic Block Model and its degree-corrected variant. We find that, across sectors, inventor networks are denser and more clustered than organization ones - consistently with the presence of small recurrent teams embedded into broader institutional hierarchies - whereas organization networks have a neater role-based structures, with few bridging firms coordinating the most peripheral ones; still, both are characterized by the presence of local core-periphery structures. We also find that the discovered meso-structures are connected to innovation output. In particular, Lorenz curves of forward citations show a pervasive inequality in technological influence: across sectors and methods, both inventor (especially) and organization networks consistently show high levels of concentration of citations in a few of the discovered clusters. Our results demonstrate that the baseline modularity-based method may not be capable of fully capturing the way collaborations drive the spreading of inventive impact across technological domains. This is due to the presence of local hierarchies that call for the more refined tools of Bayesian inference.

Figures

Figures reproduced from arXiv: 2601.10224 by Andrea Mina, Andrea Vandin, Anna Gallo, Lorenzo Emer, Mattia Marzi, Tiziano Squartini.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A large-scale dataset of Android applications and their SDK dependencies

    cs.SE 2026-07 conditional novelty 5.5

    A reproducible static-analysis pipeline yields 334k app-version observations of 99k Android apps linked to 246 tracking SDKs and 197 providers, released with code and networks.

Reference graph

Works this paper leans on

70 extracted references · 3 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Hub-driven, national innovation systems (China, Korea), dominated by large corporate- academic clusters such as Huawei, Samsung and KAIST 12 clusters

    Maximization of the modularity The first, and most representative, method of the aforementioned class is the one prescribing to maximize modularity, defined as Q = 1 2L NX i=1 X j aij − kikj 2L δgigj , (3) 10 Sector Modularity maximization BIC-SBM minimization BIC-dcSBM minimization AI 9 clusters. Hub-driven, national innovation systems (China, Korea), do...

  2. [2]

    Minimization of the Bayesian Information Criterion BIC is an information criterion widely employed to compare statistical models [55]: it embodies a trade- off between accuracy and complexity, penalizing models with too many parameters. More formally, the BIC of a probabilistic model with log-likelihood L is defined as BIC = κ ln n − 2L, (4) where κ denot...

  3. [3]

    Characterization of the partitions In order to describe the composition of the partition identified by each algorithm, we perform complementary analyses at the levels of individuals and organizations, further characterizing each cluster through a set of indi- cators that summarize its internal organization. More specifically, we compute the cluster-specif...

    2021

  4. [4]

    W. W. Powell, K. W. Koput, and L. Smith-Doerr, Ad- ministrative Science Quarterly 41, 116 (1996)

    1996

  5. [5]

    Freeman, Cambridge Journal of Economics 19, 5 (1995)

    C. Freeman, Cambridge Journal of Economics 19, 5 (1995)

    1995

  6. [6]

    Uzzi, Administrative Science Quarterly 42, 35 (1997)

    B. Uzzi, Administrative Science Quarterly 42, 35 (1997)

    1997

  7. [7]

    Girvan and M

    M. Girvan and M. E. Newman, Proceedings of the na- tional academy of sciences 99, 7821 (2002)

    2002

  8. [8]

    M. E. Newman, Proceedings of the national academy of sciences 103, 8577 (2006)

    2006

  9. [9]

    V. D. Blondel, J.-L. Guillaume, R. Lambiotte, and E. Lefebvre, Journal of Statistical Mechanics: Theory and Experiment 2008, P10008 (2008)

    2008

  10. [10]

    Acemoglu, U

    D. Acemoglu, U. Akcigit, and W. R. Kerr, Proceedings of the National Academy of Sciences 113, 11483 (2016)

    2016

  11. [11]

    Ramahandry, V

    T. Ramahandry, V. Bonneau, E. Bani, N. Vlasov, M. Flickenschild, O. Batura, N. Tcholtchev, P. L¨ ammel, and M. Boerger, Key Enabling Technologies for Europe’s Technological Sovereignty, Tech. Rep. PE 697.184 (Panel for the Future of Science and Technology (STOA), Euro- pean Parliamentary Research Service, Brussels, 2021)

    2021

  12. [12]

    Stanford emerging technology review 2025,

    S. University, “Stanford emerging technology review 2025,” https://setr.stanford.edu (2025), accessed July 2025

    2025

  13. [13]

    Chellappa, G

    R. Chellappa, G. Madhavan, T. E. Schlesinger, and J. L. Anderson, PNAS Nexus 4, pgaf030 (2025)

    2025

  14. [14]

    M. F. Safitra, M. Lubis, T. F. Kusumasari, and D. P. Putri, Procedia Computer Science 234, 381 (2024)

    2024

  15. [15]

    W. W. Powell, D. R. White, K. W. Koput, and J. Owen- Smith, American Journal of Sociology 110, 1132 (2005)

    2005

  16. [16]

    A. L. Oliver, Research Policy 33, 583 (2004)

    2004

  17. [17]

    Kapoor and P

    R. Kapoor and P. J. McGrath, Research Policy 43, 555 (2014)

    2014

  18. [18]

    Huggins, A

    R. Huggins, A. Johnston, M. Munday, and C. Xu, Sci- ence and Public Policy 50, 531 (2023)

    2023

  19. [19]

    L. D. Browning, J. M. Beyer, and J. C. Shetler, Academy of Management Journal 38, 113 (1995)

    1995

  20. [20]

    Market value and patent citations: A first look,

    B. H. Hall, A. B. Jaffe, and M. Trajtenberg, “Market value and patent citations: A first look,” (2000)

    2000

  21. [21]

    M. E. J. Newman, Networks: An Introduction , 2nd ed. (Oxford University Press, Oxford, UK, 2018)

    2018

  22. [22]

    M. E. Newman and J. Park, Physical review E68, 036122 (2003)

    2003

  23. [23]

    Wasserman and K

    S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge university press, 1994)

    1994

  24. [24]

    D. J. Watts, Small worlds: the dynamics of networks be- tween order and randomness (Princeton university press, 1999)

    1999

  25. [25]

    Fortunato and D

    S. Fortunato and D. Hric, Physics reports 659, 1 (2016)

    2016

  26. [26]

    B. S. Khan and M. A. Niazi, arXiv preprint arXiv:1708.00977 (2017), 10.48550/arXiv.1708.00977

    Pith/arXiv arXiv doi:10.48550/arxiv.1708.00977 2017

  27. [27]

    Park and M

    J. Park and M. E. J. Newman, Physical Review E 70, 66117 (2004)

    2004

  28. [28]

    Bianconi, Europhysics Letters 81, 28005 (2007)

    G. Bianconi, Europhysics Letters 81, 28005 (2007)

    2007

  29. [29]

    Fronczak, ArXiv (2012), doi.org/10.48550/arXiv.1210.7828

    A. Fronczak, ArXiv (2012), doi.org/10.48550/arXiv.1210.7828

    Pith/arXiv arXiv doi:10.48550/arxiv.1210.7828 2012

  30. [30]

    Squartini and D

    T. Squartini and D. Garlaschelli, Maximum-Entropy Net- works. Pattern Detection, Network Reconstruction and Graph Combinatorics (Springer International Publish- ing, 2017) p. 116

    2017

  31. [31]

    Karrer and M

    B. Karrer and M. E. Newman, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 83, 016107 (2011)

    2011

  32. [32]

    T. P. Peixoto, Advances in network clustering and block- modeling , 289 (2019)

    2019

  33. [33]

    Barab´ asi, Nature435, 207 (2005)

    A.-L. Barab´ asi, Nature435, 207 (2005)

    2005

  34. [34]

    Quantifying decentralization,

    B. S. Srinivasan and L. Lee, “Quantifying decentralization,” https://news.earn.com/ quantifying-decentralization-e39db233c28e (2017), accessed: YYYY-MM-DD

    2017

  35. [35]

    J. H. Lin, E. Marchese, C. J. Tessone, and T. Squartini, Chaos, Solitons & Fractals 164, 112620 (2022)

    2022

  36. [36]

    D. J. Jackson, What is an Innovation Ecosystem , Tech. Rep. 1(2) (National Science Foundation, Arlington, V A, 2011)

    2011

  37. [37]

    Bercovitz and M

    J. Bercovitz and M. Feldman, Research Policy 40, 81 (2011)

    2011

  38. [38]

    T´ oth, S

    G. T´ oth, S. Juh´ asz, Z. Elekes, and B. Lengyel, European Planning Studies 29, 2252 (2021)

    2021

  39. [39]

    Guimer` a, B

    R. Guimer` a, B. Uzzi, J. Spiro, and L. A. N. Amaral, Science 308, 697 (2005)

    2005

  40. [40]

    Inoue, K

    H. Inoue, K. Nagayoshi, and K. Yamaguchi, PLoS ONE 10, e0121973 (2015)

    2015

  41. [41]

    A. M. Petruzzelli, D. Rotolo, and V. Albino, Technolog- ical Forecasting and Social Change 91, 208 (2015)

    2015

  42. [42]

    Uzzi and J

    B. Uzzi and J. Spiro, American Journal of Sociology 111, 447 (2005)

    2005

  43. [43]

    Wuchty, B

    S. Wuchty, B. F. Jones, and B. Uzzi, Science 316, 1036 (2007)

    2007

  44. [44]

    Fritsch, M

    M. Fritsch, M. Piontek, and M. Titze, Industry and In- novation 27, 630 (2020)

    2020

  45. [45]

    L. G. Zucker and M. R. Darby, Proceedings of the Na- tional Academy of Sciences 93, 12709 (1996)

    1996

  46. [46]

    J. G. March, Organization Science 2, 71 (1991)

    1991

  47. [47]

    M. A. Schilling and C. C. Phelps, Management Science 53, 1113 (2007)

    2007

  48. [48]

    R. K. Merton, Science 159, 56 (1968)

    1968

  49. [49]

    Orbis intellectual property,

    Moody’s Analytics, “Orbis intellectual property,” https: //orbisip-r1.bvdinfo.com/version-20250624-1-0/ OrbisIntellectualProperty/1/Patents/Search (2025)

    2025

  50. [50]

    P. N. Gal, Measuring Total Factor Productivity at the Firm Level using OECD-ORBIS , OECD Economics 14 Department Working Papers 1049 (OECD Publishing, Paris, 2013)

    2013

  51. [51]

    Bajgar, G

    M. Bajgar, G. Berlingieri, S. Calligaris, C. Criscuolo, and J. Timmis, Coverage and representativeness of Orbis data, OECD Science, Technology and Industry Working Papers 2020/06 (OECD Publishing, Paris, 2020)

    2020

  52. [52]

    Chung and L

    F. Chung and L. Lu, Annals of combinatorics 6, 125 (2002)

    2002

  53. [53]

    Guimera, M

    R. Guimera, M. Sales-Pardo, and L. A. N. Amaral, Phys- ical Review E—Statistical, Nonlinear, and Soft Matter Physics 70, 025101 (2004)

    2004

  54. [54]

    B. H. Good, Y.-A. De Montjoye, and A. Clauset, Phys- ical Review E—Statistical, Nonlinear, and Soft Matter Physics 81, 046106 (2010)

    2010

  55. [55]

    Fortunato and M

    S. Fortunato and M. Barthelemy, Proceedings of the na- tional academy of sciences 104, 36 (2007)

    2007

  56. [56]

    T. P. Peixoto, Physical Review X 4, 011047 (2014)

    2014

  57. [57]

    T. P. Peixoto, Physical Review E 95, 012317 (2017)

    2017

  58. [58]

    K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. (Springer, New York, NY, 2002)

    2002

  59. [59]

    C. E. Shannon, Bell System Technical Journal 27, 379 (1948)

    1948

  60. [60]

    Zhang, Y

    Y. Zhang, Y. Qian, Y. Huang, Y. Guo, G. Zhang, and J. Lu, Scientometrics 111, 1925 (2017)

    1925

  61. [61]

    M. O. Lorenz, Publications of the American Statistical Association 9, 209 (1905)

    1905

  62. [62]

    F. A. Cowell, Measuring Inequality (Oxford University Press, Oxford, UK, 2011)

    2011

  63. [63]

    World Intellectual Property Organization, WIPO Tech- nology Trends 2019: Artificial Intelligence (World Intel- lectual Property Organization, Geneva, 2019)

    2019

  64. [64]

    Grassano, L

    N. Grassano, L. Napolitano, R. M’barek, E. Ro- driguez Cerezo, and J. Lasarte Lopez, Exploring the Global Landscape of Biotech Innovation: Preliminary In- sights from Patent Analysis , JRC137266 (Publications Office of the European Union, Luxembourg, 2024)

    2024

  65. [65]

    Adams, R

    P. Adams, R. Fontana, and F. Malerba, Research Policy 42, 1 (2013)

    2013

  66. [66]

    Squartini and D

    T. Squartini and D. Garlaschelli, New Journal of Physics 13, 083001 (2011)

    2011

  67. [67]

    Di Vece, E

    M. Di Vece, E. Agrimi, S. Tatullo, T. Gili, M. Ib´ a˜ nez-Berganza, and T. Squartini, arXiv preprint arXiv:2508.00542 (2025), https://arxiv.org/abs/2508.00542

    Pith/arXiv arXiv 2025

  68. [68]

    W. M. Rand, Journal of the American Statistical Asso- ciation 66, 846 (1971)

    1971

  69. [69]

    Jaccard, Bulletin de la Soci´ et´ e Vaudoise des Sciences Naturelles 37, 547 (1901)

    P. Jaccard, Bulletin de la Soci´ et´ e Vaudoise des Sciences Naturelles 37, 547 (1901)

    1901

  70. [70]

    Danon, A

    L. Danon, A. D ´ ıaz-Guilera, J. Duch, and A. Arenas, Journal of Statistical Mechanics: Theory and Experi- ment 2005, P09008 (2005). 15 Appendix A: Classification of Artificial Intelligence, Biotechnology and Semiconductors patents To identify the patents belonging to artificial intelligence, biotechnology and semiconductor technologies, we adopted the fo...

    2005