MVGraph: Benchmarking LVLMs on Evidence Composition across Multi-View Visual Graph

Yingjie Zhu; Han Cheng; Xuefeng Bai; Youcheng Pan; Yang Xiang; Kehai Chen

cs.CVOct 9, 2026

MVGraph: Benchmarking LVLMs on Evidence Composition across Multi-View Visual Graph

Authors: Yingjie Zhu, Han Cheng, Xuefeng Bai, Youcheng Pan, Yang Xiang, Kehai Chen

Organizations: Harbin Institute of Technology, Shenzhen, China · Peng Cheng Laboratory, Shenzhen, China

Abstract

We introduce MVGraph, a benchmark for evaluating large vision-language models (LVLMs) on multi-graph reasoning where the evidence required by a query is distributed across multiple interrelated visual graph views. Although such evidence commonly resides in source-specific graphs, temporal snapshots, or local observations, existing graph reasoning benchmarks remain confined to a single self-contained structure, assessing only graph perception and reasoning while leaving the alignment and composition of evidence across views underexplored. MVGraph comprises 8k instances spanning 8 graph-theoretic tasks, abstracted from two multi-graph scenarios (partial and temporal graph views). Each problem is programmatically constructed and verified to be unsolvable from a single view. Beyond end-to-end evaluation, we decompose multi-graph reasoning into four complementary capabilities---Perception, Alignment, Composition, and Reasoning---and design 29 diagnostic tasks with 64k instances to probe each one, along with golden intermediate representations for evaluating the intermediate process. Across 15 LVLMs, we reveal the difficulty of multi-graph reasoning and identify cross-view edge alignment and relation-level composition as prominent bottlenecks through stage-oriented diagnostics. Meanwhile, temporal constraints and increasing view counts expose further capability boundaries. Code and data are available at https://github.com/AAAndy-Zhu/MVGraph.

Figures & tables

Figure 1: Illustration of evidence-fragmented visual graph reasoning in MVGraph , where three views provide complementary path segments.

Figure 2: Overview of MVGraph . Left: End-to-end graph-theoretic tasks span partial and temporal graph views. Right: Stage-oriented diagnostic tasks probe perception, alignment, composition, and reasoning.

Task group	# Tasks	# Instances	Views	Avg. views	Avg. nodes	Avg. edges
Graph-Theoretic	8	8,000	2–4	3.06	14.77	34.03
Perception	1	36,000	2–8	4.46	21.47	26.93
Alignment	10	10,000	2–8	4.89	24.07	28.49
Composition	8	8,000	2–8	4.81	25.33	24.67
Reasoning	10	10,000	2–8	3.43	16.19	30.98
Total	37	72,000	2–8	–	–	–

Table 1: Statistics of MVGraph .

Models	Partial graph views				Temporal graph views				Avg.
Models	TS	MF	BM	HP	STS	MFC	SBM	THP	Avg.
Qwen3.5-9B	0.1	0.3	36.9	40.0	0.0	30.2	0.2	0.4	13.5
Gemma-4-12B-it	0.0	5.5	60.6	43.1	0.1	45.3	0.4	8.7	20.5
GLM-4.6V-Flash	0.0	0.7	7.2	4.7	0.0	46.5	0.0	0.0	7.4
Ovis2.5-9B	0.0	0.2	18.5	2.3	0.0	41.3	0.0	0.2	7.8
Qwen3.8-Flash †	35.0	54.0	97.0	77.0	8.0	59.0	8.0	65.0	50.4

Table 2: Accuracy (%) on end-to-end graph-theoretic tasks of MVGraph in thinking mode.

\dagger

denotes models accessed via API. The best result in each column within each model group is bolded.

Models	Partial				Temporal						Avg.
Models	A-SN	A-VSN	A-SE	A-VSE	A-AN	A-RN	A-AE	A-RE	A-PN	A-PE	Avg.
Qwen3.5-9B	82.1	94.0	55.2	36.0	98.1	92.1	29.8	35.5	99.6	75.5	69.8
Gemma-4-12B-it	81.3	91.0	57.1	29.8	98.4	91.9	46.5	44.9	95.0	80.6	71.7
GLM-4.6V-Flash	97.9	68.0	58.8	11.0	81.7	59.9	18.4	19.1	96.9	62.9	57.5
Ovis2.5-9B	69.4	65.7	53.4	4.0	86.1	72.0	8.3	12.6	92.2	65.9	53.0
Qwen3.8-Flash †	99.0	99.5	74.5	57.5	99.5	99.0	63.0	65.0	100.0	89.5	84.7

Table 3: Accuracy (%) of thinking-mode LVLMs on the ten alignment tasks of MVGraph .

\dagger

denotes models accessed via API. The best result in each column is bolded.

Models	Partial						Temporal		Avg.
Models	C-UN	C-UE	C-PA	C-CD	C-MVS	C-EV	C-PP	C-TPC	Avg.
Qwen3.5-9B	94.1	33.7	95.0	77.5	99.1	99.2	98.0	58.5	81.9
Gemma-4-12B-it	92.0	43.1	91.0	72.0	91.3	90.7	98.5	36.0	76.8
GLM-4.6V-Flash	68.0	21.9	58.5	32.5	70.4	69.3	96.5	6.5	53.0
Ovis2.5-9B	60.6	16.8	40.0	40.0	66.3	63.0	96.5	1.0	48.0
Qwen3.8-Flash †	99.0	67.0	98.0	89.5	99.5	99.5	100.0	87.0	92.4

Table 4: Accuracy (%) of thinking-mode LVLMs on the eight composition tasks in MVGraph .

\dagger

denotes models accessed via API. The best result in each column is bolded.

Models	Partial					Temporal					Avg.
Models	R-TS	R-MF	R-BM	R-HP	R-BN	R-STS	R-MFC	R-SBM	R-THP	R-CE	Avg.
Qwen3.5-9B	72.0	62.0	79.0	87.0	93.0	0.0	46.0	0.0	1.0	97.0	53.7
Gemma-4-12B-it	91.0	41.0	71.0	89.0	97.0	0.0	67.0	5.0	44.0	96.0	60.1
GLM-4.6V-Flash	0.0	2.0	9.0	3.0	50.5	0.0	52.0	0.0	0.0	65.5	18.2
Ovis2.5-9B	2.0	14.0	25.0	5.0	56.5	0.0	34.0	0.0	0.0	62.5	19.9
Qwen3.8-Flash †	93.0	73.0	93.0	86.0	87.0	16.0	70.0	28.0	65.0	69.5	68.1

Table 5: Accuracy (%) of thinking-mode LVLMs on the ten structure-prepared reasoning tasks in MVGraph . Models receive textualized structural evidence instead of graph images.

\dagger

denotes models accessed via API. The best result in each column is bolded.

Figure 5: Diagnostic performance with thinking-mode across various number of graph views. The reasoning includes only Bridge-Node Criticality (R-BN) and Causal Edge Identification (R-CE).

Figure 6: Effect of view availability on MVGraph performance, where Full uses all graph views, Single View retains one randomly selected view, and Leave-One-Out removes that same view. Bars show mean accuracy on the sampled instances.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

ID	Task	Example question	Example answer
Partial graph views
TS	Topological Sorting	Merge all views into a directed acyclic graph and return a valid topological ordering of every node.	[E13, E9, E63, E11, E4, E10, E3, E18, E8, E48, E43, E53]
MF	Maximum Flow	After merging all capacity-network views, what is the maximum flow from source E4 to sink E6 ?	46
BM	Bipartite Matching	Given the displayed applicant and job partitions, return a maximum-cardinality matching in the merged graph.	[(E11, E2), (E33, E8), (E35, E3), (E43, E80), (E55, E38), (E58, E1)]
HP	Hamiltonian Path	Merge all views and return a path that visits every node in the resulting graph exactly once.	[E9, E11, E67, E63, E13, E5, E70, E61, E12, E1, E7, E52, E80, E32]
Temporal graph views

Appendix

Table 6: Examples of the eight end-to-end graph-theoretic reasoning tasks. For tasks admitting multiple valid solutions, one valid answer is shown. Long structured answers are abbreviated for readability.

ID	Task	Example question	Example answer
Partial graph views
A-SN	Shared Nodes	Identify the node labels that are present in all graph views.	[E4, E61]
A-VSN	View-Specific Nodes	List the nodes that are exclusive to Graph 3.	[E30]
A-SE	Shared Edges	What edge triples are shared by every graph view?	[[E11, R1, E56]]
A-VSE	View-Specific Edges	What edge triples are unique to Graph 1 across the given graph views?	[[E1, R4, E61], [E4, R1, E71], [E15, R2, E61]]
Temporal graph views

Appendix

Table 7: Examples of the ten Alignment tasks. For tasks admitting multiple valid solutions, one valid answer is shown. Long structured answers are abbreviated for readability.

ID	Task	Example question	Example answer
Partial graph views
C-UN	Union Node Count	How many unique node labels appear in the union of all graph views?	22
C-UE	Union Edge Count	Across all graph views, how many different edge triples are shown?	28
C-PA	Path Assembly	After merging all graph views, give one path from E28 to E21 as an ordered list of edge triples.	[[E28, R1, E77], [E77, R2, E58], [E58, R3, E13], [E13, R4, E50], [E50, R1, E78], [E78, R2, E21]]
C-CD	Component Decomposition	After merging all graph views, list every connected component with its nodes and edge triples.	component: nodes [E13,E19,E22,E27, E28,E38,E44]; edges [[E13,R1,E27], …] component: nodes [E26,E45,E58,E78]; edges [[E26,R3,E45], …]
C-MVS	Minimal View Set	Which graph views form the smallest sufficient set for connecting E5 to E76?	[1, 2]

Appendix

Table 8: Examples of the eight Composition tasks. For tasks admitting multiple valid solutions, one valid answer is shown. Long structured answers are abbreviated for readability.

ID	Task	Example question	Example answer
Partial graph views
R-TS	Topological Sorting	Merge all views into a directed acyclic graph and return a valid topological ordering of every node.	[E45, E63, E72, E22, E31, E65, E47, E48, E7, E30, E44, E49, E24, E62]
R-MF	Maximum Flow	After merging all capacity-network views, what is the maximum flow from source E37 to sink E79 ?	55
R-BM	Bipartite Matching	Given the applicant and job partitions in the graph facts, return a maximum-cardinality matching in the merged graph.	[(E24, E11), (E39, E3), (E5, E6), (E51, E17), (E62, E35), (E63, E47), (E66, E28), (E76, E38)]
R-BN	Bridge-Node Criticality	Which cross-view node(s) act as necessary bridges on the route from E60 to E47 ?	[E28, E31, E75]
R-HP	Hamiltonian Path	Merge the graph facts into one undirected graph and return a path that visits every node exactly once.	[E10, E16, E59, E33, E5, E22, E72, E3, E27, E49, E28, E39, E50, E73, E18, E55, E30]

Appendix

Table 9: Examples of the ten reasoning tasks. For tasks admitting multiple valid solutions, one valid answer is shown. Long structured answers are abbreviated for readability.

ID	Task	Instances	Views	Avg. views	Avg. nodes	Avg. edges
Partial graph views
TS	Topological Sorting	1,000	2–4	2.98	13.01	36.23
MF	Maximum Flow	1,000	2–4	2.98	12.00	25.54
BM	Bipartite Matching	1,000	2–4	3.02	18.00	34.28
HP	Hamiltonian Path	1,000	2–4	3.03	15.51	40.91
Temporal graph views

Appendix

Table 10: Per-task statistics for the end-to-end graph-theoretic challenges. Average node and edge counts are computed after deduplication across all views of an instance.

ID	Task	Instances	Views	Avg. views	Avg. nodes	Avg. edges
Partial graph views
A-SN	Shared Nodes	1,000	2–8	4.78	33.10	47.51
A-VSN	View-Specific Nodes	1,000	2–8	4.76	32.91	40.19
A-SE	Shared Edges	1,000	2–8	4.72	33.90	44.91
A-VSE	View-Specific Edges	1,000	2–8	4.72	32.71	41.10
Temporal graph views

Appendix

Table 11: Per-task statistics for the alignment diagnostics.

ID	Task	Instances	Views	Avg. views	Avg. nodes	Avg. edges
Partial graph views
C-UN	Union Node Count	1,000	2–8	4.71	32.51	39.72
C-UE	Union Edge Count	1,000	2–8	4.70	32.70	39.67
C-PA	Path Assembly	1,000	2–8	4.75	29.48	24.91
C-CD	Component Decomposition	1,000	2–8	4.75	12.73	10.22
C-MVS	Minimal View Set	1,000	2–8	4.79	31.41	26.45

Appendix

Table 12: Per-task statistics for the composition diagnostics.

ID	Task	Instances	Views	Avg. views	Avg. nodes	Avg. edges
Partial graph views
R-TS	Topological Sorting	1,000	2–4	2.98	13.01	36.23
R-MF	Maximum Flow	1,000	2–4	2.98	12.00	25.54
R-BM	Bipartite Matching	1,000	2–4	3.02	18.00	34.28
R-HP	Hamiltonian Path	1,000	2–4	3.03	15.51	40.91
R-BN	Bridge-Node Criticality	1,000	2–8	4.78	29.69	25.08

Appendix

Table 13: Per-task statistics for the structure-prepared reasoning diagnostics. The eight graph-theoretic tasks reuse the underlying instances in Table 10 , but supply structural information rather than requiring visual graph reconstruction.

Model	TS	STS	MF	MFC	BM	SBM	HP	THP	Avg.
No-Thinking
Gemma-4-12B-it	0.0	0.0	0.0	40.9	0.0	0.1	4.0	0.0	5.6
Qwen3.5-9B	0.0	0.0	0.0	41.5	0.0	0.0	0.2	0.0	5.2
Ovis2.5-9B	0.0	0.0	0.0	41.7	0.0	0.0	0.3	0.0	5.2
Qwen3-VL-8B	0.0	0.0	0.0	42.3	0.0	0.0	1.0	0.0	5.4
GLM-4.6V-Flash	0.0	0.0	0.0	41.7	0.0	0.0	0.0	0.0	5.2

Appendix

Table 14: Performance of LVLMs on the 8 end-to-end graph-theoretic reasoning tasks of MVGraph , where

\dagger

denotes evaluation via API called. The best results are bolded .

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