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Analyzing the progress of Indian states chasing sustainable development goals using complex network framework

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Applying the generalized economic-complexity (GENEPY) algorithm to India's official state-level SDG scores, this paper claims that SDG 9 (Industry, Innovation, and Infrastructure) is the highest-weight goal and Kerala the leading state.

desk verdict Straightforward application of a known network method to NITI Aayog's SDG India data; the new subnational rankings are plausible, but the paper skips verification of its linearized eigenproblem, provides no code or data, and overreaches on a few interpretive claims. read the letter →

arxiv 2501.05314 v1 pith:PKKFBLWW submitted 2025-01-09 econ.GN physics.soc-phq-fin.EC

Hrishidev Unni , Rubal Rathi , Sangita Dutta Gupta , Anirban Chakraborti This is my paper · ORCID
classification econ.GNphysics.soc-phq-fin.EC
keywords sustainabledevelopmentgoalsIndiabipartitenetworkeconomiccomplexityGENEPYeigenvectorcentralitySDG9state-levelranking
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

The paper tries to extract a signal from India's official state-level SDG scores that a simple average hides: which states have the capability to achieve difficult goals, and which goals are hard enough that only capable states reach them. It applies the SDGs-GENEPY algorithm, which treats the 36 states and union territories and the 16 scored goals as the two sides of a weighted bipartite network and computes a complexity score for each side. The headline empirical result is that SDG 9 (Industry, Innovation, and Infrastructure) carries the largest goal weight, with SDG 2, SDG 5, and SDG 13 also prominent, while Kerala ranks first among states. The new state rankings correlate positively but only weakly with the official composite index, so the method changes the picture, not just the labels. If the result stands, it would give policymakers a data-driven way to see which SDGs are structurally harder and which states deserve targeted support on those goals.

What carries the argument

The central object is a weighted bipartite network whose adjacency matrix is $I_{sg}(\tau)$, the score of state $s$ on goal $g$ in year $\tau$. The GENEPY iteration updates state complexity $D_s$ and goal complexity $C_g$ through coupled equations: $D_s$ sums a state's scores weighted by goal complexity, while $C_g$ is a harmonic mean of state scores weighted by inverse state complexity. The paper follows the earlier result that this iteration can be linearized: $D_s$ becomes the principal eigenvector of the state similarity matrix $U=NN^\top$ and $C_g$ the principal eigenvector of $V=N^\top N$, where $N_{sg}=I_{sg}/(k_s k'_g)$ is the score normalized by the state's total score and the goal's adjusted score. The reported goal weights are $W_g=C_g/k'_g$. This machinery turns the raw scores into centrality measures and gives a quantitative ranking for both nodes in the bipartite network.

What would settle it

A reader could rerun the algorithm on the same score matrix after replacing every score by its rank, which preserves all orderings but destroys the ratio structure. If the goal weights or state complexity ranks change materially under that transformation, the interval-scale premise is false and the rankings are not supported by the data.

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Extended reading notes

Core claim

On its own terms, the discovery is that the GENEPY algorithm, run on four editions of the official state-goal score matrix (2018, 2019, 2020-21, 2023-24), yields a ranked list of states and a ranked list of goals that are not the same as the official composite ranking. For the most recent year, the largest goal weight is assigned to SDG 9; the other high-weight goals include SDG 2, SDG 5, and SDG 13. Among states, Kerala sits at the top of the complexity ranking. The authors interpret these scores as centralities in a bipartite network, showing that more complex states achieve more complex goals in the Indian federal context, and they argue the weighted performance profiles reveal where each state is strong or weak after accounting for goal difficulty.

Load-bearing premise

The entire ranking rests on treating the official 0-100 goal scores for each state as real, comparable numbers, so that taking averages, products, and ratios of them inside the complexity algorithm is meaningful; if the scores are only rough orderings or use different rubrics for different goals, the complexity ranks and goal weights are artifacts.

Editorial extensions

If this is right

  • States that rank high on the official average but low on the complexity score are exposed as performers on easy goals whose capability is narrow, while the reverse holds for states that do comparatively well on high-weight goals.
  • Multiplying raw scores by goal weights, as in the paper's weighted performance figures, provides a direct visual and numerical diagnostic of which goals drag each state down.
  • Recomputing ranks each year, as done for 2018-2024, tracks how administrative splits such as the creation of new states and union territories change the relative complexity landscape.
  • Future editions of the official index can be plugged into the same algorithm, allowing continuous monitoring of whether goals become easier or harder over time.

Reading between the lines

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

  • The paper does not test this, but because GENEPY rewards goals achieved selectively by high-complexity states, SDG 9's top weight may reflect the wide spread of industrial and infrastructural performance across states rather than any inherent national priority; a goal on which all states scored alike would receive a low weight no matter how important it is.
  • A natural check, absent from the paper, would be to rerun the algorithm on rank-transformed or winsorized scores; if the goal weights and state rankings lurch under such a transformation, the interval-scale assumption is doing all the work.
  • The weak correlation with the official composite suggests that adopting complexity weights would reallocate policy attention, but whether that reallocation improves SDG outcomes is an empirical question this paper does not answer.
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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 / 6 minor

Summary. The paper applies the SDG-GENEPY framework, previously introduced by Sciarra et al., to NITI Aayog SDG India Index scores for 36 Indian states and union territories across four editions (2018, 2019, 2020-21, and 2023-24). The states and SDGs are treated as a weighted bipartite network, and the authors compute state complexity scores as principal eigenvectors of a similarity matrix, derive goal weights, and rank states accordingly. The headline results are that SDG 9 (Industry, Innovation, and Infrastructure) receives the largest weight, Kerala ranks first among states, and the proposed rankings correlate only weakly with the official NITI Aayog rankings. The paper also presents evolutions of state ranks and goal weights over the four years.

Significance. If the computations are correct, the paper offers a useful, policy-relevant application of a known network-complexity method to subnational SDG data. The data are public and the method is standard, so the results are in principle reproducible; the paper does not, however, provide code or machine-checked proofs. The finding that SDG 9 dominates, and the identification of top-performing states, could inform Indian SDG discussions. The contribution is primarily empirical rather than methodological, and the current manuscript leaves several load-bearing technical points unverified, so the significance is conditional on those points being resolved.

major comments (4)
  1. [Methodology and The SDGs-GENEPY framework] The paper asserts, without derivation or numerical evidence, that the nonlinear iteration for D_s and C_g can be replaced by the principal eigenvectors of U = NN' and V = N'N. The displayed iterative equations include normalization factors ν_s and ν_g that do not appear in the eigenproblem, and the definition of k_s is printed as ∑_s I_sg(τ) rather than ∑_g I_sg(τ), so the exact object being computed is ambiguous. Since the headline finding that SDG 9 has the largest weight W_g (Results and Discussion, second paragraph) is an output of this eigenvector computation, the manuscript should either supply the equivalence proof/citation for this dataset or compare the eigenvector solution to the fixed point of the nonlinear map (e.g., by iterating the equations to convergence). Without this check, the central ranking claim is not established.
  2. [Datasets and Results and Discussion (Figures 4-5)] The intertemporal comparison is compromised by non-comparable inputs. The data section states that the 2018 edition used 62 indicators and excluded goals 11, 12, and 13 (while goal 14 is always excluded), whereas later editions used 100-115 indicators and a different goal set. The number of states and union territories also changes across years (e.g., Telangana and Ladakh were created). The paper nonetheless presents 'evolution of ranks' and 'evolution of weights' across the four years as if they were comparable. The authors should restrict the analysis to a common set of goals (and, where possible, states) or explicitly quantify the effect of the changing goal set on the computed weights; otherwise the temporal claims in Figures 4 and 5 are not supported.
  3. [Results and Discussion, paragraph 2] The paper claims 'there is a positive correlation between this study’s index and the NITI Aayog rankings, the relationship remains weak,' but no correlation coefficient, statistical test, or supporting figure is provided anywhere in the manuscript. This is a specific, testable claim about the validity of the proposed index; the authors should report, for each year, the rank correlation (e.g., Spearman's ρ) between D_s and k_s, with a confidence interval or p-value.
  4. [All results (Figures 2-5)] No uncertainty or sensitivity analysis is reported. The complexity scores and goal weights are deterministic functions of the NITI Aayog score matrix, but those scores are themselves averages of indicator scores with NITI-defined target normalizations, and small perturbations in the scores could alter the eigenvector rankings. Because the paper's contribution is precisely the ranking of states and goals, the authors should assess robustness, for instance by bootstrapping over indicators within goals, jackknifing states, or perturbing scores, and report the stability of the top-ranked states and of the SDG 9 weight.
minor comments (6)
  1. [Datasets] The first sentence contains 'NITI The Aayog' and the text later refers to 'NIF' instead of 'NITI'; please correct these typographical errors.
  2. [Introduction] Reference [26] is cited as 'Sciarra et al.25' in the introduction; the reference numbering should be checked and corrected.
  3. [Datasets] The paper says the data contain scores in '16 sustainable development goals' but also excludes goal 14 always and goals 11, 12, and 13 in 2018; these statements are inconsistent and should be reconciled (the 2018 edition would then cover 13 goals, not 16).
  4. [Methodology] The iterative equations for fD and fC include a division by ν_s and ν_g whose purpose is not explained; please define these normalization factors and clarify how they are absorbed in the eigenproblem formulation.
  5. [Results and Discussion] There are several figure-cross-reference errors: the weights are said to be shown in 'Figure 3c' instead of Figure 2C, and 'Kc ranks' should likely read 'k_s ranks'; please standardize figure labels and notation throughout.
  6. [Abstract] The abstract states the study 'enables data-driven policy-making,' but the paper does not translate its results into concrete policy recommendations; consider adding a short policy implications subsection or softening the claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the GENEPY analysis is a parameter-free application of a published, externally sourced algorithm to NITI Aayog scores, and no central claim reduces to a fitted input or to a self-citation chain.

full rationale

The derivation chain is explicit and self-contained once the NITI Aayog scores are accepted: I_sg(τ) enters the definitions k_s = Σ_g I_sg and k'_g = Σ_s I_sg/k_s, then N_sg = I_sg/(k_s k'_g), then U = NN' and V = N'N, and the principal eigenvectors D_s and C_g are computed; finally W_g = C_g/k'_g. Every step is a deterministic function of the input scores, with no parameter fitted to a target result and no outcome reused to define the algorithm. The only external authority invoked is the Sciarra et al. GENEPY framework, and those citations are not self-citations because none of the present authors overlaps with Sciarra, Chiarotti, Ridolfi, or Laio. The statement that the nonlinear iteration can be approximated by an eigenproblem is imported from that prior work rather than rederived, which raises a correctness or reproducibility concern—especially because the paper does not verify that the eigenvector matches the iterative fixed point and because k_s is misprinted as summing over s rather than g. However, an unverified or even inaccurate approximation is not circularity: the reported ranking of SDG 9 is still computed from the data and the stated method, not assumed from the conclusion. The observation that W_g is later used to reweight the same scores I_sg is also not a logical circularity; it is a data-driven reweighting, and the weight itself is not an input to its own computation. The paper is therefore best scored 0 on the circularity scale, with the linearization and typographical ambiguities flagged as robustness issues rather than circular steps.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper introduces no free parameters fitted to data and no invented entities. Its assumptions are the comparability of NITI Aayog scores as interval-scale measurements, the validity of the Perron-Frobenius eigenvector computation, and the faithfulness of the linearized approximation to the nonlinear algorithm. These are standard but unexamined assumptions for this application.

assumptions (3)
  • domain assumption NITI Aayog normalized SDG indicator scores (0-100) are interval-scale comparable across states, goals, and years.
    The GENEPY algorithm multiplies and inverts these scores; if the scores are ordinal or not comparable across goal-specific rubrics, the complexity scores and weights are not meaningful. Invoked in 'Datasets'.
  • standard math The matrices U and V are nonnegative and their principal eigenvectors exist and are unique, providing well-defined rankings.
    Perron-Frobenius conditions are assumed; scores are nonnegative so the matrices are nonnegative, but irreducibility is not shown. Invoked in 'The SDGs-GENEPY framework' when computing eigenvectors.
  • domain assumption The linearized eigenvector solution faithfully represents the nonlinear iterative Fitness-Complexity scheme.
    Sciarra et al. (2021) established this for the original formulation; the paper adopts it without re-deriving it for this dataset. Invoked in 'Methodology'.

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Cite this review

Pith. "Pith review of Analyzing the progress of Indian states chasing sustainable development goals using complex network framework." pith.science (2026). https://pith.science/paper/PKKFBLWW

@misc{pith2026250105314,
  author       = {Pith},
  title        = {Pith review of: Analyzing the progress of Indian states chasing sustainable development goals using complex network framework},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKKFBLWW}},
  note         = {Machine review of arXiv:2501.05314}
}
read the original abstract

The Sustainable Development Goals (SDGs) offer a critical global framework for addressing challenges like poverty, inequality, climate change, etc. They encourage a holistic approach integrating economic growth, social inclusion, and environmental sustainability to create a better future. We aim to examine India's responsibility in achieving the SDGs by recognizing the contributions of its diverse states in the federal structure of governance. As the nodal agency in India, the NITI Aayog's existing SDG index, using various socioeconomic indicators to determine the performance across different goals, serves as a foundation for assessing each state's progress. Building on the seminal works of Hidalgo and Hausmann (2009) and Tachhella et al. (2012), which introduced the economic complexity/fitness index, Sciarra et al. (2020) proposed the SDGs-Generalized Economic Complexity (GENEPY) framework to quantify "complexity" by computing "ranks for states" and "scores for goals", treating them as part of a complex bipartite network. In this paper, we apply the SDGs-GENEPY, to evaluate the progress and evolution of Indian states and union territories over several years. This enables us to identify each state's capacity (and rank) in achieving the SDGs. We can interpret these complexity scores as "centrality measures" of a complex bipartite network of the states and the goals. This enhances our understanding of the complex relationship between state capabilities and the achievability of SDGs within the Indian context and enables data-driven policy-making.

Figures

Figures reproduced from arXiv: 2501.05314 by the authors.

Figure 1
Figure 1. NITI Aayog dataset. In sub-figure A, The data matrix (Isg(2024)) consisting of 36 states + union territories and their respective scores in each of the sustainable development goals is visualised by mapping the values to a colourmap. The higher values are towards green and the lower values are towards yellow. In sub-figure B, Indian states and union territories are coloured according to their rankings based on the s… view at source ↗
Figure 2
Figure 2. SDGs-GENEPY framework. A subset of the underlying weighted bipartite network with 8 sample states (Andaman and Nicobar(AN), Kerala(KL), Telangana (TG), Gujarat(GJ), Mizoram(MZ), Jharkhand(JH), Bihar(BR) and Ladak(LA)) is visualized in the sub-figure B. The edges are coloured and drawn according to the weight of the links (Isg(2024)) where the thicker and greener edges represent a stronger performance of a state in t… view at source ↗
Figure 3
Figure 3. Weighted performance of states across goals. After multiplying the weights of the goals that we have calculated with the performance of each state in each goal as Isg(2024) ∗Wg and the new weighted performances of all states are plotted. For comparison, the states are divided into 3 groups based on their NITI-Aayog ranks, and the average of their performances are also plotted as thicker lines along with the national… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Evolution of ranks. Evolutions of ranks of the states through the 4 years (2018,2019,2020,2024) of data obtained from ks(τ) as well as Ds(τ) are plotted. Sub-figure A represents the evolution of ks(τ) ranks (which are equivalent to the NITI-Aayog ranks) and sub-figure …
Figure 5
Figure 5. Figure 5: Evolution of weights. The weights(Wg(τ)) of the goals obtained using SDGs-GENEPY framework over the four years (2018,2019,2020,2024) of data is shown as a grouped bar chart. Different groups of bars represent different SDGs and the colours of the bars in each group rep…

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