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arxiv: 2606.12581 · v1 · pith:GZGVUE2Mnew · submitted 2026-06-10 · 💻 cs.SI · cs.AI

Graph Reduction in Multirelational Networks: A Spreading-Oriented Reduction Benchmark

Mateusz Stolarski , Micha{\l} Czuba , Piotr Bielak , Piotr Br\'odka This is my paper

Pith reviewed 2026-06-27 07:20 UTC · model grok-4.3

classification 💻 cs.SI cs.AI
keywords influence maximizationgraph reductionsparsificationcoarseningmultilayer networksmultirelational networksspreading processesbenchmark
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The pith

Graph reduction preserves seed set quality on single-layer networks but causes ranking degradation on multirelational networks.

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

The paper introduces the Spreading-Oriented Reduction Benchmark (SORB) to measure how graph reduction techniques alter the accuracy of influence maximization predictions. It runs the same models on both single-layer and multilayer real-world networks while applying sparsification and coarsening before evaluation. Performance is tracked with two separate metrics, Gain@k and AUC_cutoff. The central result is that reduction effects split sharply by network type: single-layer cases tolerate sparsification for seed selection, whereas flattened multilayer cases lose ranking quality under every reduction approach tested. This matters because practitioners routinely shrink large networks before running spreading analyses, yet the downstream cost to prediction quality had not been quantified in a controlled way.

Core claim

The authors establish through the SORB pipeline that the impact of graph reduction on influence maximization is strongly dependent on network type and evaluation task: sparsification preserves seed set quality on single-layer networks, whereas flattened multilayer networks exhibit systematic ranking degradation regardless of reduction strategy.

What carries the argument

The Spreading-Oriented Reduction Benchmark (SORB) pipeline, an extensible evaluation framework that folds graph reduction steps directly into influence maximization testing on collections of single-layer and multirelational networks.

If this is right

  • Influence maximization studies must incorporate reduction steps into evaluation rather than testing algorithms on full graphs alone.
  • Sparsification can be applied to single-layer networks for computational savings with limited loss in seed set quality under Gain@k.
  • All tested reduction methods harm ranking performance on flattened multilayer networks across both Gain@k and AUC_cutoff.
  • Task-specific metrics reveal differences that single-metric evaluations would miss when reduction is involved.
  • Standardized benchmarks like SORB make the trade-off between network size and spreading prediction accuracy measurable and comparable.

Where Pith is reading between the lines

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

  • For applications on real social networks that are often multirelational, reduction may need to be avoided or replaced by methods that preserve layer structure rather than flattening.
  • The consistent degradation on multilayer cases may trace to the flattening step itself, pointing to a need for reduction operators that operate directly on multilayer representations.
  • Extending the benchmark to dynamic or temporal networks could test whether the same type-dependent patterns hold when edges appear and disappear over time.

Load-bearing premise

The chosen collection of real-world networks is representative of the networks on which influence maximization is typically applied.

What would settle it

Running the same SORB pipeline on a new collection of multirelational networks and observing no systematic ranking degradation after reduction would falsify the claim of consistent degradation in that network type.

Figures

Figures reproduced from arXiv: 2606.12581 by Mateusz Stolarski, Micha{\l} Czuba, Piotr Bielak, Piotr Br\'odka.

Figure 1
Figure 1. Figure 1: A schematic illustration of the SORB processing pipeline. The main components are: the reduction module, which preprocesses the input network; the prediction module, which executes the seed selection models specified in the configuration on both original and reduced graphs; the diffusion module, which generates the spreading results for each predicted seed set by running MICM simulations on the original ne… view at source ↗
Figure 2
Figure 2. Figure 2: Number of edges in the sparsified versions of the [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Influence maximisation model execution times with the applied re [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Memory usage during IM model execution. Left panel: peak GPU [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Gain achieved for different seed sizes on examined networks using [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Gain score for FinDKG network with the applied sparsification rate r. 3.5.2 Ranking prediction With the aim of observing and analysing the cumulative spreading potential of actors, they can be ordered in a ranking according to their estimated influence, denoted as R, similarly to the approach proposed in [4]. In this work, we refine this idea and provide a more formal presentation, as described in Def. 7. … view at source ↗
Figure 7
Figure 7. Figure 7: AUCcutoff score achieved on the examined networks by seed selection approaches preprocessed using different reduction models. From another perspective, we may also analyse which sparsification model performs best in the context of ranking prediction, as shown in [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of AUCcutoff on the timik network between the two strate￾gies for handling multilayer structure during reduction. In Tab. 7, we report the difference between the AUCcutoff obtained from pre￾dictions on the original graph and on the graph preprocessed with coarsening models. In light of the previously discussed results for these models, the de￾terioration in performance across every network and f… view at source ↗
Figure 9
Figure 9. Figure 9: Gain score for each network included in the experiments with the [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Gain score for film networks with the applied sparsification rate [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
read the original abstract

Real-world networks are inherently incomplete, noisy, and dynamically evolving, making it difficult to capture all actors and their relationships. Their scale often renders direct analysis computationally demanding. While influence maximisation (IM) has been widely studied, the role of graph reduction as a preprocessing step, and its impact on IM accuracy, remains underexplored. In this work, we introduce the Spreading-Oriented Reduction Benchmark (SORB), an open-source, standardised framework for systematically evaluating IM models across diverse task settings. SORB provides an extensible pipeline operating on a representative collection of real-world networks, including single- and multilayer structures, and accounts for graph reduction directly into the evaluation process. This design shifts the focus from analysing IM algorithms in isolation to quantifying how graph reduction alters predictive performance. Using SORB, we study the effects of sparsification and coarsening across multiple IM scenarios. Our results show that the impact of reduction is strongly dependent on both the network type (single-layer vs. multirelational) and the downstream task ($Gain@k$ vs. $\mathrm{AUC}_{\mathrm{cutoff}}$): sparsification preserves seed set quality on single-layer networks, whereas flattened multilayer networks exhibit systematic ranking degradation regardless of reduction strategy. These findings highlight the importance of reduction-aware, multi-task evaluation when studying spreading processes in complex networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces the Spreading-Oriented Reduction Benchmark (SORB), an open-source extensible pipeline for evaluating how graph reduction (sparsification and coarsening) affects influence maximization accuracy. It applies SORB to a collection of real-world single-layer and multirelational networks and reports that reduction effects depend strongly on network type and downstream task: sparsification preserves seed-set quality (Gain@k) on single-layer networks, whereas flattened multilayer networks exhibit systematic ranking degradation (AUC_cutoff) independent of reduction strategy.

Significance. If the empirical patterns are robust to broader validation, SORB could provide a needed standardized, reduction-aware framework for IM studies on complex networks. The open-source pipeline and multi-task design are positive features for reproducibility and for shifting focus from isolated algorithm performance to preprocessing effects.

major comments (2)
  1. [Abstract] Abstract (and likely Datasets section): the assertion that SORB operates on a 'representative collection' of networks lacks explicit selection criteria, any tabulated comparison of network statistics (size, density, degree heterogeneity, community structure) against standard IM benchmarks, or an argument that the chosen graphs reflect the topologies and spreading dynamics where IM is typically applied. This is load-bearing for the central claim that observed differences can be attributed to network type rather than unmeasured covariates in the specific collection.
  2. [Abstract] Abstract (and Results): the reported 'strong dependence' on network type and task, including 'systematic ranking degradation,' is presented without reference to statistical tests, confidence intervals, error bars, or controls for multiple comparisons. This makes it impossible to assess whether the contrast between single-layer preservation and multilayer degradation is statistically reliable or sensitive to post-hoc choices.
minor comments (1)
  1. [Abstract] Abstract: the notation AUC_cutoff is introduced without definition or reference to its exact computation (e.g., how the cutoff is chosen or how AUC is calculated on the reduced graph).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important areas for improving the clarity and rigor of our claims regarding the SORB benchmark. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and likely Datasets section): the assertion that SORB operates on a 'representative collection' of networks lacks explicit selection criteria, any tabulated comparison of network statistics (size, density, degree heterogeneity, community structure) against standard IM benchmarks, or an argument that the chosen graphs reflect the topologies and spreading dynamics where IM is typically applied. This is load-bearing for the central claim that observed differences can be attributed to network type rather than unmeasured covariates in the specific collection.

    Authors: We agree that the manuscript would benefit from greater transparency on network selection. In the revised version, we will expand the Datasets section with explicit selection criteria (e.g., coverage of single-layer vs. multirelational structures, range of sizes and densities, and relevance to spreading processes), include a table comparing key statistics against common IM benchmarks (such as SNAP or KONECT networks), and add a brief justification arguing that the collection captures representative topologies for influence maximization studies. revision: yes

  2. Referee: [Abstract] Abstract (and Results): the reported 'strong dependence' on network type and task, including 'systematic ranking degradation,' is presented without reference to statistical tests, confidence intervals, error bars, or controls for multiple comparisons. This makes it impossible to assess whether the contrast between single-layer preservation and multilayer degradation is statistically reliable or sensitive to post-hoc choices.

    Authors: We acknowledge the absence of formal statistical support in the current presentation. The revision will add statistical tests (e.g., non-parametric paired tests for metric differences across reduction methods), report confidence intervals or standard errors, include error bars on figures, and apply multiple-comparison corrections. These additions will be placed in the Results section to substantiate the reported patterns. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical benchmark with independent results

full rationale

The paper introduces the SORB empirical pipeline and reports observed performance differences (Gain@k and AUC_cutoff) across network types and reduction strategies on a collection of real-world graphs. No equations, fitted parameters, or derivations are presented that reduce the reported contrasts to quantities defined by the authors' own inputs. The representativeness assumption is external to the results and does not create a self-definitional or fitted-input reduction. No self-citation load-bearing steps, uniqueness theorems, or ansatzes appear in the abstract or described claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, mathematical axioms, or invented physical entities are described. The framework itself is a new software artifact rather than a postulated entity with independent evidence.

axioms (1)
  • domain assumption Real-world networks are inherently incomplete, noisy, and dynamically evolving
    Opening sentence of the abstract used to motivate the need for reduction-aware evaluation.

pith-pipeline@v0.9.1-grok · 5779 in / 1362 out tokens · 29374 ms · 2026-06-27T07:20:40.801984+00:00 · methodology

discussion (0)

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