Dynamic Graph World Modelling: Learning Future Dynamics from Temporal Context

Bo Li; Yue Yang; Yujin Huang; Siao Liu; David Lemphers; Sara E Rodriguez Gomez; Luke Borgnolo; Can Wang

cs.LGOct 14, 2026

Dynamic Graph World Modelling: Learning Future Dynamics from Temporal Context

Authors: Bo Li, Yue Yang, Yujin Huang, Siao Liu, David Lemphers, Sara E Rodriguez Gomez, Luke Borgnolo, Can Wang,

Organizations: School of Information and Communication Technology, Griffith University, Australia · Maincode, Australia · School of Computing and Information Systems, University of Melbourne, Australia · Future Science and Engineering College, Soochow University, China ·

Abstract

Dynamic graph learning models how entities and their relations evolve from historical observations to predict future graph states. Existing methods do not fully address dynamic graph world modelling, which requires learning transitions from temporal context to future latent graph states. This is difficult for three reasons: nodes and relations rely on different historical evidence, structural evolution is path-dependent, and future snapshots provide sparse and realization-specific targets. We propose Dynamic Graph World Modelling (DyG-WM), the first framework to jointly predict future node and relation representations from temporal context by answering three questions: what has evolved, how it evolved, and what will evolve next. To capture what has evolved, a historical node-relation context encoder summarizes node-neighborhood trajectories and pair-specific histories. To characterize how it evolved, a node-relation path-signature encoder captures ordered structural changes. To predict what will evolve next, a dual-level joint-embedding objective predicts target-snapshot node and relation representations without reconstructing the raw graph. Experiments on 12 link-prediction and two node-classification datasets demonstrate the effectiveness of DyG-WM across both tasks.

Figures & tables

Figure 1: Comparison of dynamic graph learning and dynamic graph world modelling. Dynamic graph learning maps historical graphs to task-specific outputs, whereas dynamic graph world modelling predicts future latent state.

Figure 2: Overview of DyG-WM . (a) The historical node-relation context encoder summarizes the trajectories of nodes and their neighborhoods and constructs pair-specific relation contexts from historical snapshots. (b) The node-relation path-signature encoder uses second-order signatures to capture ordered structural changes at both levels. (c) The dual-level joint-embedding predictive objective predicts target-snapshot node and relation representations.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	DyGFormer	CLDG	MaskDGNN	DVGMAE	DyG-WM
rnd	Wikipedia	96.55 $\pm$ 0.19	94.93 $\pm$ 0.50	92.66 $\pm$ 0.43	98.46 $\pm$ 0.05	98.60 $\pm$ 0.01	97.51 $\pm$ 0.09	97.12 $\pm$ 0.06	98.98 $\pm$ 0.01	89.50 $\pm$ 0.18	86.71 $\pm$ 0.53	83.96 $\pm$ 0.55	98.94 $\pm$ 0.02
	Reddit	98.04 $\pm$ 0.04	97.69 $\pm$ 0.51	97.97 $\pm$ 0.02	97.75 $\pm$ 0.38	99.10 $\pm$ 0.01	97.91 $\pm$ 0.04	98.03 $\pm$ 0.02	99.09 $\pm$ 0.00	96.75 $\pm$ 0.01	96.73 $\pm$ 0.02	95.72 $\pm$ 0.07	99.20 $\pm$ 0.01
	MOOC	83.16 $\pm$ 2.19	79.33 $\pm$ 4.02	86.01 $\pm$ 0.06	94.19 $\pm$ 0.73	82.05 $\pm$ 0.28	85.58 $\pm$ 0.39	84.98 $\pm$ 0.13	89.80 $\pm$ 0.23	68.17 $\pm$ 1.30	74.97 $\pm$ 0.20	71.02 $\pm$ 0.89	82.50 $\pm$ 0.39
	LastFM	70.94 $\pm$ 0.72	71.92 $\pm$ 0.84	71.54 $\pm$ 0.35	62.38 $\pm$ 2.16	85.93 $\pm$ 0.11	71.10 $\pm$ 0.32	73.59 $\pm$ 0.11	93.15 $\pm$ 0.02	64.49 $\pm$ 0.69	65.48 $\pm$ 0.66	63.00 $\pm$ 0.21	92.61 $\pm$ 0.06
	Enron	87.29 $\pm$ 1.84	85.60 $\pm$ 1.98	74.41 $\pm$ 0.73	84.87 $\pm$ 1.60	90.49 $\pm$ 0.04	83.90 $\pm$ 0.28	84.56 $\pm$ 0.24	93.46 $\pm$ 0.14	87.87 $\pm$ 0.47	85.82 $\pm$ 0.86	74.84 $\pm$ 1.19	92.55 $\pm$ 0.25
	UCI	90.35 $\pm$ 0.50	64.90 $\pm$ 9.03	82.54 $\pm$ 0.41	94.05 $\pm$ 0.37	93.93 $\pm$ 0.04	89.71 $\pm$ 2.88	91.98 $\pm$ 0.43	94.59 $\pm$ 0.22	86.18 $\pm$ 0.30	88.04 $\pm$ 0.08	88.31 $\pm$ 0.17	94.15 $\pm$ 0.17

Table 1: Transductive AUC-ROC for dynamic link prediction with random ( rnd ), historical ( hist ), and inductive ( ind ) negative edge sampling. Bold red and underlined blue emphasize best and 2nd-best results.

Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	DyGFormer	CLDG	MaskDGNN	DVGMAE	DyG-WM
Wikipedia	94.06 $\pm$ 0.23	91.46 $\pm$ 0.24	78.29 $\pm$ 0.67	97.22 $\pm$ 0.07	96.93 $\pm$ 0.02	96.74 $\pm$ 0.09	95.89 $\pm$ 0.06	97.42 $\pm$ 0.02	86.63 $\pm$ 0.42	84.35 $\pm$ 0.20	80.43 $\pm$ 1.29	97.52 $\pm$ 0.03
Reddit	96.01 $\pm$ 0.10	95.25 $\pm$ 0.29	67.96 $\pm$ 1.62	96.12 $\pm$ 0.61	96.48 $\pm$ 0.03	95.95 $\pm$ 0.09	95.36 $\pm$ 0.11	96.56 $\pm$ 0.02	94.33 $\pm$ 0.08	94.66 $\pm$ 0.06	93.26 $\pm$ 0.21	97.44 $\pm$ 0.10
MOOC	81.86 $\pm$ 0.78	79.41 $\pm$ 2.36	80.43 $\pm$ 0.30	91.44 $\pm$ 0.49	82.43 $\pm$ 0.28	82.33 $\pm$ 0.65	83.09 $\pm$ 0.18	87.92 $\pm$ 0.29	63.33 $\pm$ 0.58	72.03 $\pm$ 0.39	66.51 $\pm$ 0.95	79.63 $\pm$ 0.44
LastFM	81.89 $\pm$ 0.69	81.36 $\pm$ 1.62	76.83 $\pm$ 0.14	62.44 $\pm$ 5.05	87.88 $\pm$ 0.05	76.36 $\pm$ 1.04	80.10 $\pm$ 0.16	93.05 $\pm$ 0.05	67.08 $\pm$ 1.27	66.47 $\pm$ 1.02	63.90 $\pm$ 0.57	93.50 $\pm$ 0.22
Enron	82.81 $\pm$ 1.85	74.13 $\pm$ 2.31	69.84 $\pm$ 0.47	74.17 $\pm$ 2.79	87.60 $\pm$ 0.25	81.23 $\pm$ 0.33	77.88 $\pm$ 0.15	90.73 $\pm$ 0.10	80.10 $\pm$ 1.15	76.05 $\pm$ 1.65	62.54 $\pm$ 0.60	87.45 $\pm$ 0.26
UCI	77.47 $\pm$ 1.78	58.26 $\pm$ 6.40	77.93 $\pm$ 0.49	86.21 $\pm$ 2.79	89.65 $\pm$ 0.16	79.89 $\pm$ 0.98	88.84 $\pm$ 0.15	92.03 $\pm$ 0.09	75.80 $\pm$ 0.37	76.76 $\pm$ 0.18	77.16 $\pm$ 0.11	92.32 $\pm$ 0.13

Table 2: Inductive AUC-ROC for dynamic link prediction in the inductive (new-node) setting with random negative edge sampling. Bold red and underlined blue indicate the best and second-best results, respectively.

Metric	Dataset	Ratio	TGAT	CAWN	TCL	GraphMixer	DyGFormer	EvolveGCN-H	ROLAND	CLDG	MaskDGNN	DVGMAE	SG-JEPA	DyG-WM
Macro-F1	DBLP	40%	68.54 $\pm$ 0.60	64.71 $\pm$ 0.92	69.76 $\pm$ 1.09	71.69 $\pm$ 0.79	67.88 $\pm$ 0.72	26.10 $\pm$ 11.19	47.14 $\pm$ 20.87	60.70 $\pm$ 1.34	70.98 $\pm$ 0.84	60.36 $\pm$ 0.83	73.96 $\pm$ 0.59	75.45 $\pm$ 0.35
		60%	71.60 $\pm$ 0.61	66.32 $\pm$ 0.60	72.33 $\pm$ 0.68	73.80 $\pm$ 0.52	69.99 $\pm$ 0.62	32.22 $\pm$ 19.39	58.32 $\pm$ 13.49	59.70 $\pm$ 1.95	71.91 $\pm$ 0.24	60.36 $\pm$ 0.81	75.88 $\pm$ 0.36	77.13 $\pm$ 0.51
		80%	73.12 $\pm$ 0.56	67.66 $\pm$ 1.11	73.59 $\pm$ 0.77	75.41 $\pm$ 0.77	71.46 $\pm$ 0.80	37.47 $\pm$ 9.69	52.91 $\pm$ 12.28	61.77 $\pm$ 2.20	73.88 $\pm$ 1.21	60.38 $\pm$ 1.00	77.55 $\pm$ 0.33	78.13 $\pm$ 0.23
	Tmall	40%	47.36 $\pm$ 0.78	45.49 $\pm$ 0.35	49.12 $\pm$ 0.49	49.20 $\pm$ 0.94	33.31 $\pm$ 6.17	35.80 $\pm$ 9.81	41.46 $\pm$ 8.38	32.06 $\pm$ 1.83	48.35 $\pm$ 1.60	36.23 $\pm$ 1.02	54.16 $\pm$ 0.36	57.37 $\pm$ 0.37
		60%	49.05 $\pm$ 0.26	47.28 $\pm$ 0.56	50.10 $\pm$ 0.58	51.50 $\pm$ 0.75	32.65 $\pm$ 2.84	36.13 $\pm$ 6.82	40.87 $\pm$ 6.29	30.10 $\pm$ 1.44	50.83 $\pm$ 1.03	35.47 $\pm$ 1.19	55.81 $\pm$ 0.34	59.17 $\pm$ 0.49
		80%	49.86 $\pm$ 0.44	48.23 $\pm$ 0.82	50.56 $\pm$ 0.78	52.92 $\pm$ 0.41	34.73 $\pm$ 2.49	39.41 $\pm$ 3.33	40.74 $\pm$ 6.82	31.00 $\pm$ 1.70	51.39 $\pm$ 1.52	35.40 $\pm$ 1.30	57.24 $\pm$ 0.39	60.52 $\pm$ 0.39

Table 3: Node classification on dynamic graphs. Macro-F1 and Micro-F1 (%) on the held-out test nodes, reported as mean

\pm

std over 5 seeds at labelled-node training ratios of 40%, 60%, and 80%. Bold red and underlined blue indicate the best and second-best results, respectively.

Figure 3: Latent alignment on Can. Parl. with and without the predictive objective.

Settings	Enron	Can. Parl.	LastFM
w/o Historical Context	71.53 $\pm$ 3.02	76.08 $\pm$ 2.77	75.11 $\pm$ 0.52
w/o Path Signature	59.09 $\pm$ 5.52	60.31 $\pm$ 4.65	70.17 $\pm$ 0.87
w/o Predictive Objective	71.69 $\pm$ 3.94	75.58 $\pm$ 2.11	75.93 $\pm$ 1.32
DyG-WM	74.99 $\pm$ 1.93	78.19 $\pm$ 1.97	77.36 $\pm$ 0.73

Table 4: Results (AUC-ROC) of ablations.

Figure 4: AUC-ROC-efficiency trade-off on Reddit and LastFM.

Figure 5: Robustness to noise on Can. Parl. and Wikipedia.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Datasets	Domains	#Nodes	#Links	#N&L Feature	Bipartite	Duration	Unique Steps	Time Granularity
Wikipedia	Social	9,227	157,474	N/A & 172	True	1 month	152,757	Unix timestamps
Reddit	Social	10,984	672,447	N/A & 172	True	1 month	669,065	Unix timestamps
MOOC	Interaction	7,144	411,749	N/A & 4	True	17 months	345,600	Unix timestamps
LastFM	Interaction	1,980	1,293,103	N/A & N/A	True	1 month	1,283,614	Unix timestamps
Enron	Social	184	125,235	N/A & N/A	False	3 years	22,632	Unix timestamps
UCI	Social	1,899	59,835	N/A & N/A	False	196 days	58,911	Unix timestamps

Appendix

Table 5: Statistics of the datasets. N/A denotes the absence of node or edge features. #Nodes denotes the number of nodes.

Datasets	#Nodes	#Links	#Classes	#Snapshots	#Features
DBLP	28,085	236,894	10	27	80
Tmall	577,314	4,807,545	5	186	80

Appendix

Table 6: Statistics of the dynamic node classification datasets.

Configuration	Link prediction	Node classification
Hidden dimension	128	128
Message-passing layers	2	2
Window parameter $W$	4	3
Temporal dimension	32	32
Predictor hidden dimension	256	256
Signature order	2	2

Appendix

Table 7: Default implementation settings for DyG-WM . Dataset-specific overrides are selected using validation data only.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	DyGFormer	CLDG	MaskDGNN	DVGMAE	DyG-WM
rnd	Wikipedia	96.69 $\pm$ 0.21	95.20 $\pm$ 0.54	92.68 $\pm$ 0.47	98.54 $\pm$ 0.05	98.78 $\pm$ 0.01	97.93 $\pm$ 0.06	97.39 $\pm$ 0.05	99.06 $\pm$ 0.02	91.55 $\pm$ 0.09	88.76 $\pm$ 0.43	85.68 $\pm$ 0.62	99.10 $\pm$ 0.02
	Reddit	98.07 $\pm$ 0.02	97.71 $\pm$ 0.56	98.03 $\pm$ 0.02	97.74 $\pm$ 0.39	99.18 $\pm$ 0.01	98.09 $\pm$ 0.04	98.09 $\pm$ 0.01	99.18 $\pm$ 0.00	97.01 $\pm$ 0.02	96.97 $\pm$ 0.02	95.91 $\pm$ 0.07	99.28 $\pm$ 0.01
	MOOC	79.55 $\pm$ 2.76	75.48 $\pm$ 4.64	84.54 $\pm$ 0.05	92.81 $\pm$ 0.85	81.50 $\pm$ 0.22	85.17 $\pm$ 0.49	83.79 $\pm$ 0.16	89.26 $\pm$ 0.26	64.90 $\pm$ 1.88	72.35 $\pm$ 0.17	68.41 $\pm$ 1.18	81.94 $\pm$ 0.38
	LastFM	71.67 $\pm$ 0.90	72.38 $\pm$ 0.75	73.39 $\pm$ 0.27	62.64 $\pm$ 2.26	86.99 $\pm$ 0.04	76.82 $\pm$ 0.38	75.81 $\pm$ 0.09	93.12 $\pm$ 0.05	63.91 $\pm$ 0.63	65.76 $\pm$ 0.57	63.67 $\pm$ 0.19	92.20 $\pm$ 0.04
	Enron	84.06 $\pm$ 2.82	83.50 $\pm$ 2.64	76.08 $\pm$ 0.56	81.68 $\pm$ 2.21	89.42 $\pm$ 0.05	85.53 $\pm$ 0.30	81.62 $\pm$ 0.29	92.27 $\pm$ 0.09	86.13 $\pm$ 0.35	84.57 $\pm$ 0.68	71.82 $\pm$ 0.58	91.40 $\pm$ 0.22
	UCI	89.16 $\pm$ 0.88	60.57 $\pm$ 8.46	82.60 $\pm$ 0.44	94.19 $\pm$ 0.38	95.17 $\pm$ 0.04	91.31 $\pm$ 3.18	93.51 $\pm$ 0.28	95.88 $\pm$ 0.14	86.68 $\pm$ 0.14	87.71 $\pm$ 0.06	88.05 $\pm$ 0.10	95.26 $\pm$ 0.09

Appendix

Table 8: Transductive Average Precision (AP) for dynamic link prediction with random ( rnd ), historical ( hist ), and inductive ( ind ) negative edge sampling. bold red and underlined blue emphasize best and 2nd-best results.

Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	DyGFormer	CLDG	MaskDGNN	DVGMAE	DyG-WM
Wikipedia	94.75 $\pm$ 0.20	92.25 $\pm$ 0.22	80.33 $\pm$ 0.69	97.45 $\pm$ 0.06	97.22 $\pm$ 0.03	97.26 $\pm$ 0.08	96.33 $\pm$ 0.05	97.56 $\pm$ 0.03	89.39 $\pm$ 0.28	86.59 $\pm$ 0.20	82.19 $\pm$ 1.04	97.94 $\pm$ 0.02
Reddit	95.87 $\pm$ 0.13	95.19 $\pm$ 0.23	66.20 $\pm$ 1.64	96.24 $\pm$ 0.66	97.66 $\pm$ 0.03	96.45 $\pm$ 0.06	95.61 $\pm$ 0.08	97.74 $\pm$ 0.02	94.68 $\pm$ 0.06	95.02 $\pm$ 0.04	93.54 $\pm$ 0.18	97.90 $\pm$ 0.06
MOOC	78.67 $\pm$ 1.16	75.82 $\pm$ 3.14	79.46 $\pm$ 0.43	89.71 $\pm$ 0.64	81.86 $\pm$ 0.21	81.88 $\pm$ 1.08	81.71 $\pm$ 0.20	87.24 $\pm$ 0.30	61.43 $\pm$ 0.51	69.48 $\pm$ 0.39	65.55 $\pm$ 0.93	79.74 $\pm$ 0.48
LastFM	82.84 $\pm$ 0.84	82.01 $\pm$ 1.45	78.54 $\pm$ 0.16	62.93 $\pm$ 3.73	89.44 $\pm$ 0.04	80.93 $\pm$ 0.78	81.98 $\pm$ 0.11	92.22 $\pm$ 0.09	66.60 $\pm$ 1.18	67.66 $\pm$ 0.63	65.99 $\pm$ 0.41	92.61 $\pm$ 0.17
Enron	80.62 $\pm$ 2.01	70.73 $\pm$ 1.73	71.10 $\pm$ 0.35	72.08 $\pm$ 2.32	86.31 $\pm$ 0.21	82.54 $\pm$ 0.40	76.70 $\pm$ 0.16	89.89 $\pm$ 0.13	76.55 $\pm$ 1.20	74.24 $\pm$ 1.44	59.32 $\pm$ 0.79	86.75 $\pm$ 0.56
UCI	78.46 $\pm$ 3.21	58.76 $\pm$ 6.47	79.51 $\pm$ 0.30	87.78 $\pm$ 2.28	92.10 $\pm$ 0.09	82.22 $\pm$ 1.31	90.91 $\pm$ 0.13	92.99 $\pm$ 0.06	76.78 $\pm$ 0.32	77.92 $\pm$ 0.24	77.93 $\pm$ 0.15	93.38 $\pm$ 0.18

Appendix

Table 9: Inductive Average Precision (AP) for dynamic link prediction in the inductive (new-node) setting with random negative edge sampling. Bold red and underlined blue indicate the best and second-best results, respectively.

Figure 6: Latent alignment with and without the predictive objective in the Wikipedia dataset.

Figure 7: Latent alignment with and without the predictive objective in the UCI dataset.

Panel of Figure 8 — Figure 8: Accuracy-efficiency trade-off across all dynamic link prediction datasets. Each panel reports AUC-ROC against training time.

	$\displaystyle\mathcal{L}_{\mathrm{JEPA}}={}$	$\displaystyle\lambda_{N}\mathcal{L}^{N}+\lambda_{R}\mathcal{L}^{R}$		(13)
		$\displaystyle+\lambda_{\mathrm{var}}\left(\mathcal{L}_{\mathrm{var}}^{N}+\mathcal{L}_{\mathrm{var}}^{R}\right)+\lambda_{\mathrm{cov}}\left(\mathcal{L}_{\mathrm{cov}}^{N}+\mathcal{L}_{\mathrm{cov}}^{R}\right).$		(13)

Appendix

Algorithm 2 Dual-level joint-embedding predictive training

Dynamic Graph Learning

Dynamic graph learning models how networks and their node features change over time to predict links, events, labels, and system behavior.

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WorldGraph: Graph-Native World Modeling

Zezhong Ding, Yipeng Li, Xike Xie

School of Artificial Intelligence and Data Science, University of Science and Technology of China (USTC) · Data Darkness Lab, Suzhou Institute for Advanced Research, USTC · School of Biomedical Engineering, USTC

World Model Learning World Models Dynamic Graph Learning

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World models infer latent states of an environment to capture its underlying dynamics and predict future evolution. Many real-world environments, however, are inherently relational and observed as evolving graphs, where entities, relations, and their properties change over time. Prior graph-related world models use graph structures to organize internal states or support task-specific reasoning, rather than treating an evolving graph itself as the modeled world. We instead study graph world modeling (GWM), where graph evolution itself constitutes the world dynamics. We formulate graph world modeling over observed graph evolution, latent graph states, and heterogeneous graph-transition predictions. Based on this formulation, we construct GWM-Zero, a benchmark covering node-, edge-, and graph-level transitions over eight temporal graph datasets. We propose WorldGraph, which combines a state-aware graph transformer for multi-granularity structural and transition-conditioned evolution modeling with transition-aware GRPO using dynamic grouping and structure-aware verifiable rewards. Extensive experiments on GWM-Zero show that WorldGraph consistently outperforms representative graph representation, temporal graph learning, graph pretraining, and graph world-model baselines across all three transition granularities.

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