Graph Data Augmentation via Contrastive Generator Inversion ($\texttt{DCBA}$)

Mateusz Stolarski; Michał Czuba; Łukasz Kraiński; Katarzyna Musial; Paweł Prałat; Bogumił Kamiński; Piotr Bródka

cs.LGOct 5, 2026

Graph Data Augmentation via Contrastive Generator Inversion ( $\texttt{DCBA}$ )

Authors: Mateusz Stolarski, Michał Czuba, Łukasz Kraiński, Katarzyna Musial, Paweł Prałat, Bogumił Kamiński, Piotr Bródka

Organizations: Wrocław University of Science and Technology · University of Technology Sydney · SGH Warsaw School of Economics · Toronto Metropolitan University

Abstract

Graphs provide a natural representation of many complex systems, ranging from social platforms to ecosystems. However, the development of graph-based machine learning methods is often constrained by the limited availability of large and diverse graph datasets. In this paper, we introduce $\texttt{DCBA}$ , a model-based approach to graph data augmentation that infers the configuration of a synthetic graph generator from an observed network. We instantiate the proposed framework using the $\texttt{ABCD}$ generator, which produces scale-free networks with community structure. Our model learns a joint representation of graphs and generator parametrisations using a multi-positive contrastive objective with soft negative weighting. The learned representation enables the prediction of an $\texttt{ABCD}$ configuration whose stochastic realisations preserve the macrostructural properties encoded by the generator. Experiments show that $\texttt{DCBA}$ recovers generator parameters more accurately and robustly than an algorithmic inverse-modelling baseline. Its downstream utility is further demonstrated in community detection, where inferred configurations used to fine-tune $\texttt{PRoCD}$ improve AMI on average by $161\%$ on synthetic and $273\%$ on real-world networks.

Figures & tables

Symbol	Sampling range	Description
$n$	$[1\,000,\ 10\,000]$	Number of nodes in the graph.
$t_{1}$	$[2.0,\ 3.0]$	Power-law exponent of the degree distribution.
$d_{\min}$	$[10^{-10},\ 0.005]\cdot n$	Minimum node degree.
$d_{\max}$	$[0.005,\ 0.5]\cdot n$	Maximum node degree.
$t_{2}$	$[1.0,\ 2.0]$	Power-law exponent of the community-size distribution.
$c_{\min}$	$[10^{-10},\ 0.05]\cdot n$	Minimum community size.

Table 1: Sampling ranges used to construct the dataset. Graph-size-dependent parameters are drawn as fractions of

n

and subsequently converted to valid integer-valued parameters of ABCD+o .

Figure 1: Architecture of DCBA . During training, ABCD configurations

\theta

and their graph realisations

G

are mapped by

e_{\phi_{\theta}}

and

e_{\phi_{G}}

, respectively, into a shared latent space. Representations originating from the same configuration are pulled together, whereas those of different configurations are pushed apart with a strength proportional to their distance in the configuration space. A soft-clustering pool assigns vertices to

K

latent slots and summarises their embeddings

\mathit{cl}_{e}

and sizes

\mathit{cl}_{s}

independently of slot order. At inference, only the path

f_{\phi}=d_{\phi_{D}}\circ e_{\phi_{G}}

is used to recover

\hat{\theta}

from an observed graph.

	Casual test set					Hard test set
Param.	Base-T	Base-L	DCBA	DCBA Comm	DCBA Comm64	Base-T	Base-L	DCBA	DCBA Comm	DCBA Comm64
$n$	1.000	1.000	0.964	0.948	0.951	1.000	1.000	0.930	0.808	0.704
$t_{1}$	-5.425	-5.425	0.959	0.914	0.927	-66.760	-66.760	0.666	0.489	0.606
$d_{\min}$	1.000	1.000	0.971	0.946	0.970	1.000	1.000	0.946	0.791	0.731
$d_{\max}$	0.661	0.661	0.801	0.740	0.779	0.449	0.449	0.590	0.680	0.470
$t_{2}$	-2.031	-16.130	0.007	0.105	0.089	-86.160	-36.430	-0.012	-0.082	0.204

Table 2: Parameter-wise

R^{2}

on the casual and hard test sets; first- and second-best results within each split are shown in dark and pale green, respectively; the bottom row reports the overall mean.

Mode	Fine-tuning corpus	AMI	$\Delta$ B	$p$
B	none (frozen checkpoint)	$0.189$	–	–
R	random ABCD graphs	$0.378$	$+0.189$	$0.0057$
D	inferred $\hat{\theta}$ with DCBA	$\mathbf{0.493}$	$\mathbf{+0.304}$	$\mathbf{<10^{-4}}$
O	ground-true $\theta$	$0.541$	$+0.351$	$<10^{-4}$

Table 3: Community detection with PRoCD on unseen ABCD graphs under different fine-tuning regimes. AMI is averaged while

\Delta

B and

p

compare each regime with B using a paired Wilcoxon test.

Graph	Pretrained	Base-L	DCBA	$\sigma$
PolBlogs [ 1 ]	$0.021$	$0.020$	$\mathbf{0.291}$	$0.000$
Newsgroup 5cl-1 [ 33 ]	$0.018$	$0.025$	$\mathbf{0.031}$	$0.000$
Newsgroup 5cl-2 [ 33 ]	$0.112$	$0.194$	$\mathbf{0.263}$	$0.053$
Newsgroup 5cl-3 [ 33 ]	$0.096$	$0.226$	$\mathbf{0.236}$	$0.001$
EuroSiS [ 31 ]	$\mathbf{0.603}$	$0.602$	$\mathbf{0.603}$	$0.000$
Cora-Full: OS [ 28 ]	$\mathbf{0.199}$	$0.187$	$\mathbf{0.199}$	$0.000$

Table 4: Community detection with PRoCD on six real-world networks from [ 14 ] under different fine-tuning regimes, measured by average AMI against ground-truth communities with standard deviation over three runs for the best-performing regime.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	GIN	GPS	GPS-weighted	GPS-clustered	GPS-clustered-weighted
$n$	0.36	0.93	0.86	0.95	0.89
$t_{1}$	0.68	0.95	0.94	0.87	0.95
$d_{\min}$	0.84	0.92	0.94	0.96	0.96
$d_{\max}$	0.01	0.74	0.76	0.78	0.78
$t_{2}$	-0.02	0.00	-0.05	-0.02	-0.02
$c_{\min}$	0.13	0.46	0.15	0.44	0.44

Appendix

Table 5: Parameter-wise

R^{2}

on the casual test set for the compared graph encoders; first- and second-best results are shown in green.

Parameter	K-64	K-128	K-256
$n$	0.86	0.89	0.81
$t_{1}$	0.94	0.95	0.92
$d_{\min}$	0.95	0.96	0.94
$d_{\max}$	0.70	0.78	0.75
$t_{2}$	0.01	-0.02	0.01
$c_{\min}$	0.32	0.44	0.38

Appendix

Table 6: Parameter-wise

R^{2}

on the casual test set for varying numbers of clusters

K

; first- and second-best results are shown in green.

Parameter	Q-wide	Q-0	Q-coarse	Q-top	Q-uniform
$n$	0.89	0.92	0.94	0.92	0.94
$t_{1}$	0.95	0.94	0.95	0.95	0.92
$d_{\min}$	0.96	0.94	0.95	0.95	0.93
$d_{\max}$	0.78	0.79	0.82	0.78	0.73
$t_{2}$	-0.02	-0.02	-0.02	-0.01	-0.01
$c_{\min}$	0.44	0.45	0.50	0.37	0.39

Appendix

Table 7: Parameter-wise

R^{2}

on the casual test set for varying cluster-size quantile sets

Q

; first- and second-best results are shown in green.

Parameter	identity	n-max	relative	log	empirical
$n$	0.98	0.98	0.98	0.89	0.98
$t_{1}$	-11.72	0.78	0.87	0.95	0.90
$d_{\min}$	0.32	-1.26	-0.32	0.96	-0.20
$d_{\max}$	0.80	0.81	0.82	0.78	0.80
$t_{2}$	-6.97	-0.04	-0.04	-0.02	-0.02
$c_{\min}$	0.31	0.29	-0.03	0.44	0.13

Appendix

Table 8: Parameter-wise

R^{2}

on the casual test set for the compared configuration scalers; first- and second-best results are shown in green.

Parameter	base	comm
$n$	0.89	0.91
$t_{1}$	0.95	0.92
$d_{\min}$	0.96	0.96
$d_{\max}$	0.78	0.78
$t_{2}$	-0.02	0.07
$c_{\min}$	0.44	0.80

Appendix

Table 9: Parameter-wise

R^{2}

on the casual test set for constant (

\mathbf{X}=\mathbf{1}

) and community-size node features; first- and second-best results are shown in green.

Parameter	Batch 32	Batch 64
$n$	0.91	0.94
$t_{1}$	0.92	0.94
$d_{\min}$	0.96	0.96
$d_{\max}$	0.78	0.74
$t_{2}$	0.07	0.13
$c_{\min}$	0.80	0.86

Appendix

Table 10: Parameter-wise

R^{2}

on the casual test set for the compared mini-batch sizes; first- and second-best results are shown in green.

Figure 2: Distribution of pairwise

z_{G}

embedding distances for same-instance vs. cross-instance replica pairs, log-scaled density.

Panel of Figure 3 — Figure 3: $\mathbb{R}^{2}$ representation of $z_{G}$ with $t_{2}$ (left) and $\xi$ (right) colour overlay.

Figure 4: Eigenvalue spectrum (left) and per-parameter eigenvector loadings (right) of $M_{\theta}$ matrix.

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Graph Neural Networks (GNNs) are powerful models for handling attributed graphs in tasks such as classification, link prediction, and community detection, as they enable the aggregation of information from both structural and semantic sources. However, progress in community detection is hindered by the lack of high-quality datasets, since ground-truth community labels are often unavailable and most algorithms proposed in recent literature rely on the same benchmark datasets for model training and evaluation. To address this issue, attributed random graph generators are commonly employed to create synthetic graphs for assessing the strengths and limitations of GNN-based models. Nevertheless, most existing generators rely heavily on power-law degree distributions, despite recent evidence indicating that scale-free networks are rare, particularly in social network contexts. Moreover, state-of-the-art attributed graph generators provide limited flexibility, as they do not allow users to construct communities with varying densities, degree distributions, and sub-community structures. To overcome these limitations, we introduce the Synthetic Community-Aware Attributed Graph Generator (SynCo), a graph generation algorithm that allows users to control the node degree distribution and sub-community structure. We evaluate SynCo across three different tasks: graph mimicking, hyperparameter evaluation, and node clustering tuning. The results show that our model outperforms state-of-the-art approaches in synthetic graph generation and data augmentation, while preserving the original distributions of duplicated and augmented datasets, as confirmed by statistical tests well know in literature. We also demonstrate the ability of SynCo to generate nodes in large scale, up to 2.1 million nodes.

Abstract

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