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REVIEW 5 major objections 5 minor 157 references

Diffusion Models for Influence Maximization on Temporal Networks: A Guide to Make the Best Choice

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A structured taxonomy and flowchart can select the right diffusion model for influence maximization on temporal networks.

desk verdict Useful survey with a broken selection table: the LT submodularity error undermines the guide's core advice. read the letter →

arxiv 2507.22589 v1 pith:S2NUSC4T submitted 2025-07-30 cs.SI

Aaqib Zahoor , Iqra Altaf Gillani , Janibul Bashir This is my paper · ORCID
classification cs.SI
keywords temporalnetworksinfluencemaximizationdiffusionmodelsseedselectionsubmodularitymonotonicitymodelsocial
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 argues that choosing a diffusion model for influence maximization on temporal networks can be reduced to a structured decision procedure instead of an ad hoc literature search. It builds a taxonomy of diffusion models, organized as process-, interaction-, competition-, structure-, and target-oriented, and attaches to each model its network type and the properties of its influence-spread function: monotonicity and submodularity. A flowchart then routes a user from problem definition to model class to a concrete model, depending on whether the priority is maximizing spread or minimizing computation. If the guide is right, a practitioner can map any application scenario to a recommended model and know whether greedy approximation guarantees apply.

What carries the argument

The load-bearing object is the property tables (Tables III to VII) combined with the Figure 2 flowchart. Each table entry pairs a diffusion model with its network type and whether its spread function is submodular and monotone, and those two properties are what license greedy seed selection with the $(1 - 1/e)$ guarantee. The flowchart uses the taxonomy's five categories as decision branches and routes the user to the optimization sections depending on whether the goal is maximum spread or minimal computational cost.

What would settle it

Take a model listed in Tables III to VII with a checkmark for submodularity or monotonicity, enumerate all seed sets on a small temporal network, and check whether the marginal-gain inequality holds for every pair of nested seed sets; a single violation would invalidate the optimization advice for that row. For the LT contradiction specifically, computing the exact spread function on a two-node temporal graph with repeated edges would show whether Table III's cross for LT matches the section text that calls LT monotone and submodular.

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Extended reading notes

Core claim

The central claim is that model selection for temporal influence maximization is a solvable decision problem: with a taxonomy and a property table, the best model for a given scenario can be identified systematically. The paper classifies models by underlying mechanism and evaluates each on network type, submodularity, and monotonicity, where monotone means adding seeds never shrinks expected spread and submodular means marginal gains diminish as the seed set grows. It further claims that the classic greedy $(1 - 1/e)$ approximation transfers to a temporal model exactly when its spread function is monotone and submodular, and that many temporal variants forfeit these properties, so heuristics, reverse influence sampling, and budget-aware incremental methods become the practical route. It supports this with a demonstration on the Rural Malawi contact dataset: the same seed set yields lower spread under the temporal version of the Independent Cascade model than under the static version, showing that static optimization does not carry over automatically.

Load-bearing premise

The guide's recommendations inherit the per-model labels in Tables III to VII for network type, submodularity, and monotonicity, and the paper's own text already casts doubt on those labels: it states that IC and LT influence functions are monotone and submodular while Table III marks LT as neither.

Editorial extensions

If this is right

  • A user who follows Figure 2 can go from a stated objective, whether maximizing spread or minimizing cost, to a shortlist of models without re-deriving the properties of each model.
  • For models labelled monotone and submodular, greedy or lazy-forward algorithms with the $(1 - 1/e)$ approximation guarantee are the recommended optimization route.
  • For temporal models labelled non-submodular or non-monotone, the guide directs users to heuristics, reverse influence sampling, or budget-aware incremental methods rather than vanilla greedy selection.
  • The static-versus-temporal demonstration implies that seed sets chosen on an aggregated static network will generally be suboptimal on the temporal network, so temporal structure must enter model selection itself.

Reading between the lines

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

  • The guide's usefulness depends on the accuracy of the property labels, so a reader applying it should verify the monotonicity and submodularity entry for a specific model against the cited source before trusting a greedy guarantee.
  • The tables already contain enough structured features to drive an automated model recommender: given network type, temporal regime, and objective, a ranked list of candidate models could be generated directly from the taxonomy.
  • The paper's own cpSI-R and TBCELF entries hint at a direction the guide does not fully develop: reinforcement, reactivation, and budget constraints can preserve or restore submodular structure in temporal settings, which would make greedy methods viable where the taxonomy currently marks them unsafe.
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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

5 major / 5 minor

Summary. Zahoor, Gillani, and Bashir present a survey intended to help practitioners choose diffusion models for influence maximization on temporal networks. The paper proposes a five-class taxonomy (process-, interaction-, competition-, structure-, and target-oriented models), a decision flowchart (Figure 2), and a model-selection framework (Section VI) that maps objectives (maximize spread vs. minimize computation) and application scenarios (Sections VII-VIII) to specific models. It also contains an illustrative experiment (Figure 3) comparing static vs. temporal IC spread on a contact dataset. The core deliverable is the structured guide; its correctness hinges on the property labels (submodularity, monotonicity, network type) in Tables III-VII.

Significance. The survey addresses a real need: the temporal-network influence-maximization literature is fragmented, and a structured decision-support tool could be valuable to practitioners. The taxonomy is broad in coverage and the authors make a credible attempt to organize a large literature, including both classical models and recent temporal variants. The paper also has the merit of including a small empirical demonstration (Figure 3) that static and temporal settings yield different spreads for the same seed sets. However, the guide's central artifact—the property tables and the flowchart that depends on them—is undermined by internal inconsistencies and unsupported entries. The paper cannot be accepted until the factual basis of the tables is corrected and verified; the current inconsistencies mean a reader following the guide could receive wrong optimization advice (e.g., for the LT model). If fixed, the survey could be a useful reference.

major comments (5)
  1. [Table III; Section III.A; Section VII.A] Table III marks the Linear Threshold (LT) model [67] as Submodular=× and Monotone=× for 'Static and Temporal', and similarly marks DLT as non-submodular/non-monotone. This directly contradicts Section III.A, which states that under the classical IC and LT models the influence function σ(S) is monotone and submodular, a result proved in the cited reference [67] (Kempe et al., 2003). Section VII.A repeats the incorrect statement that 'the Linear Threshold (LT) model, despite not rendering the objective function to be submodular or monotone'. Since Section VI.B and Figure 2 direct users to greedy algorithms with (1−1/e) guarantees only for models labeled submodular and monotone, the LT row is load-bearing: if the label is wrong, the optimization advice for LT is wrong; if the authors intended a temporal variant, the row needs a qualifier and the 'Static and Temporal' annotation must be corrected. This internal inconsistency must be resolved.
  2. [Tables III-VII] The submodularity and monotonicity columns in Tables III-VII are presented as facts but carry no per-entry citation, proof, or even a statement of the set function to which the property applies. For epidemic models (SI, SIR, SIS, SEIR), the ground set and the influence function are not defined, so the ✓/× entries are not interpretable. The LT case above shows that at least one entry is wrong, and because the flowchart's greedy-safety recommendations in Section VI.B depend on these labels, the entire label matrix needs justification. At minimum, the authors should state for each model what σ(S) is, whether they mean the static or temporal version, and cite a theorem or give a counterexample for each entry.
  3. [Section I.C] Section I.C says the flowchart directs users to consult 'either Section VI A (for computational efficiency optimization) or Section VI B (for spread maximization strategies)'. This is the reverse of what Figure 2 and the Section VI headings state: Section VI.A is 'Maximizing Influence Spread' and Section VI.B is 'Optimizing Computational Efficiency'. The manuscript's navigation instructions are therefore inconsistent with its own decision tool, undermining the usability of the guide.
  4. [Tables XIII-XIV; Sections VII-VIII] The use-case tables and Section VIII introduce model names that never appear in the taxonomy or reference list, including AtIic, MIM, TSI, Time-LT, DEM-IM, and SocInf in Table XIV and IES2 and S-SEIR in Sections VII.E and VIII.A. These are recommended to practitioners without definition or citation, so the central promise of the guide—an actionable selection—cannot be fulfilled for these entries. The authors should either define and reference these models, or remove them from the recommendations.
  5. [Section V.B; Section VIII.A] The recommendations for the authors' own models cpSI-R [144] and TBCELF [145] are asserted without supporting derivation. For example, Section V.B states that cpSI-R's 'monotonic and submodular properties enable efficient optimization', and Table XIII recommends cpSI-R for reinfection dynamics, but no proof or independent test is given in the manuscript. Similarly, TBCELF is recommended for budget-constrained interventions without comparing it with other cost-aware methods in the survey. Since the guide's purpose is principled model choice, these entries need a verifiable basis (proof or experimental comparison), not only a citation to the authors' papers.
minor comments (5)
  1. [General] Typographical and grammatical errors are frequent; examples include 'However. unlike' in Section I, 'appraoch' in Section III, 'Suspectible Infected Recovered' in Section V, 'Efeective' in the Table V caption, and inconsistent comma spacing in 'V t1 1, Vt2 2' in Definition 5.
  2. [Section VI.A] Reference [29] is cited for both Hawkes Process Diffusion (HPD) and OM-WTD, but [29] is the non-Markovian opinion dynamics paper by Chu et al.; the HPD attribution appears unsupported. Similarly, [92] is cited for Temporal Independent Cascade (TIC), but [92] is Murata et al.'s dynamic degree discount and RIS paper; the citation-model correspondence should be checked throughout.
  3. [Figure 3] The caption reports n=86 and e=355 (static) and e=102292 (temporal) but does not state whether the curves are means across Monte Carlo runs, nor give error bars or statistical significance; the claim that static and temporal seeds differ would be stronger with such details.
  4. [Section V.C] The introductory paragraph says predictive models are further classified into threshold and cascading models, but Table III's 'Type' column mixes Predictive, Epidemic, Explanatory, Threshold, and Cascading; the narrative and the table should be aligned.
  5. [Figure 2] The flowchart boxes 'Infection Spread Optimization' and 'Optimize Computational Power' use different wording from the corresponding Section VI headings ('Maximizing Influence Spread', 'Optimizing Computational Efficiency'); harmonizing the labels would reduce confusion.

Circularity Check

2 steps flagged · score 4.0 of 10

Two load-bearing recommendations for the authors' own models (cpSI-R, TBCELF) rest on self-citations; the rest of the taxonomy is independent, and the LT submodularity contradiction is a correctness issue, not circularity.

  1. self citation load bearing [Section V.B (Extensions); used in Section VIII.A and Table XIII]
    "Zahoor et al. [144] proposed Continuous Persistent Susceptible-Infected Model with Reinforcement and Re-activation (cpSI-R) ... Moreover, the model’s monotonic and submodular properties enable efficient optimization for seed selection, aligning well with theoretical guarantees in influence maximization."

    The guide's recommendation of cpSI-R for reinfection/immune-persistence scenarios (Section VIII.A, Table XIII: 'Diseases with reinfection dynamics and immune persistence effects ... cpSI-R') and its placement in the submodular/monotone safe-greedy set (Table III: cpSI-R [144] Temporal ✓ ✓) depend on the model's monotonicity/submodularity. The only support offered is the authors' own arXiv preprint [144]; the paper gives no proof, external benchmark, or independent citation for these properties. The selection advice therefore reduces to the authors' self-assertion about their own model.

  2. self citation load bearing [Section VI.B (Optimizing Computational Efficiency), reinforced in Section VIII.A and Tables V, XIII, XIV]
    "The TBCELF algorithm [145] exemplifies cost-aware optimization by enforcing budget constraints during temporal seed selection, thus enhancing both coverage and scalability."

    TBCELF [145] is the authors' own model. The flowchart (Figure 2) and Section VI.B route budget-constrained users to cost-aware lazy-forward optimization, and Tables XIII/XIV recommend TBCELF for targeted interventions and viral-spread seed selection. Its claimed properties (submodular/monotone in Table V, cost-effectiveness in Section VI.B) are cited only to the authors' own CODS-COMAD paper, with no independent evaluation in this manuscript. The 'best choice' output for budget-constrained scenarios is thus justified by the authors' self-citation rather than by an external derivation or benchmark.

full rationale

This is a survey/guide rather than a mathematical derivation, so most of the claimed organization is not circular in the Eq.-X-equals-Eq.-Y sense. The taxonomy and flowchart are self-contained as a classification exercise, and the majority of model entries cite external papers. The only load-bearing circular steps are the two recommendations for the authors' own models: cpSI-R and TBCELF are marked submodular/monotone and recommended on the strength of self-citations, with no proof or independent check in the paper; the guide's choices for reinfection dynamics and budget-constrained interventions therefore reduce to the authors' assertions about their own work. I do not count the LT contradiction (Table III marks LT [67] as non-submodular/non-monotone while Section III.A correctly states classical LT is monotone and submodular, and [67] is the paper proving that) as circularity: it is an internal-consistency/correctness problem in the label matrix, not a self-referential derivation. For that reason the score is moderate rather than high.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The survey contributes no fitted equations, so the free-parameter count is limited to the illustrative experiment. The main epistemic load is carried by assertions imported from the cited literature (submodularity labels, performance figures) and by the paper's own classification schema, which is assumed to be exhaustive. The authors' prior models cpSI-R and TBCELF are treated as validated inputs even though the supporting manuscript (arXiv:2412.20936) is internal to the authors.

free parameters (1)
  • IC propagation probability p = 0.01
    Hand-chosen value for the illustrative Degree Discount experiment in Section III.B; not fitted, and no sensitivity analysis is provided.
assumptions (4)
  • standard math For a monotone submodular spread function, greedy selection achieves a (1-1/e) approximation
    Invoked in Sections III and VI.B to justify greedy and RIS-based seed selection for models labeled monotone and submodular.
  • domain assumption Most temporal-network diffusion models yield non-monotone, non-submodular objective functions
    Stated in Section III and used to push practitioners toward heuristics; contradicted by the paper's own tables, which label tELT, pELT, and TBCELF as monotone and submodular.
  • ad hoc to paper The five-class taxonomy is an exhaustive partition of diffusion models
    The classification in Section V is introduced by the authors with no argument that every model fits exactly one class or that these classes capture the dimensions relevant to model choice.
  • domain assumption Repeated timestamped contacts represent distinct activation opportunities
    The Figure 3 experiment multiplies edges from 355 (static) to 102,292 (temporal) by counting repeated contacts, so the static-versus-temporal comparison mixes timing with graph density.

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Cite this review

Pith. "Pith review of Diffusion Models for Influence Maximization on Temporal Networks: A Guide to Make the Best Choice." pith.science (2026). https://pith.science/paper/S2NUSC4T

@misc{pith2026250722589,
  author       = {Pith},
  title        = {Pith review of: Diffusion Models for Influence Maximization on Temporal Networks: A Guide to Make the Best Choice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S2NUSC4T}},
  note         = {Machine review of arXiv:2507.22589}
}
read the original abstract

The increasing prominence of temporal networks in online social platforms and dynamic communication systems has made influence maximization a critical research area. Various diffusion models have been proposed to capture the spread of information, yet selecting the most suitable model for a given scenario remains challenging. This article provides a structured guide to making the best choice among diffusion models for influence maximization on temporal networks. We categorize existing models based on their underlying mechanisms and assess their effectiveness in different network settings. We analyze seed selection strategies, highlighting how the inherent properties of influence spread enable the development of efficient algorithms that can find near-optimal sets of influential nodes. By comparing key advancements, challenges, and practical applications, we offer a comprehensive roadmap for researchers and practitioners to navigate the landscape of temporal influence maximization effectively.

Figures

Figures reproduced from arXiv: 2507.22589 by the authors.

Figure 1
Figure 1. The influence research explores seed selection strategies and applies diffusion models to estimate the impact and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Flowchart showing how to pick up right diffusion model for given requirements [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Percentage influence spread on static and tempo [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Illustration of the IC model. Nodes V2 and V5 are successfully activated with probabilities Pv3v2 and Pv3v5 , respectively. V3 V2 V4 V1 V5 Wv1v3 Wv2v3 Wv3v4 Wv5v3 V2 V4 V1 V5 Wv1v3 Wv2v3 Wv3v4 Wv5v3 t=0 v3 t=1 Inactive Node Active Node [PITH_FULL_IMAGE:figures/full_fi…
Figure 5
Figure 5. Figure 5: Illustration of the LT model. Node V3 becomes active if Wv1v3 + Wv5v3 ≥ θv3 . rate β and recovery rate γ. Susceptible nodes become infected based on interactions with infected neighbors, with probability 1−e −βk, where k is the number of infected contacts. Infected nod…
Figure 6
Figure 6. Figure 6: Illustration of the SIR model. Node V3 recovers at time t = 1 with probability γ, while some susceptible nodes become infected with probability 1 − e −βk . While standard diffusion models have laid the foundational groundwork for understanding information spread, real-…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.