Eccentricity

Node regression on synthetic graphs, predicting each node’s maximum shortest-path distance to any other node. Uses synthetic topology plus task-specific source indicators or random node features. Evaluated by MSE.

Dataset details

Task

Graph eccentricity prediction — node-level task predicting max distance to any other node. The primary catalog metric is MSE.

Data

The release has 7,040 synthetic graphs with 25–35 nodes sampled from multiple graph generators: 5,120 train, 640 validation, and 1,280 test graphs.

Features

Synthetic graphs provide task-specific structural inputs such as a designated source. Targets are numeric node quantities computed by the reference algorithm; positional encodings or extra structural features are model additions.

Splits and evaluation

The fixed split is 5,120/640/1,280 graphs. The paper selects models by validation MSE and reports mean log10(MSE) over 20 runs; lower is better.

Quirks and pitfalls

Targets are deterministic functions of generated topology, so generator overlap and size range determine difficulty. Random splits test interpolation; claims about algorithmic generalization require held-out sizes or graph families.

Sources

Algorithmic Graph Tasks benchmark

SOTA Progression

Target

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard

#	Model	MSE ↓	log10(MSE)	Paper
1	GCN-SSM + k-hop GNN ★ proposed	-4.2652 ± 0.1776	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
2	MP-SSM Hyb ★ proposed	-2.9724 ± 0.0271	—	Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling no code May 2025 May '25
3	GCN-SSM + eig(Lambda) approx 1 ★ proposed	-2.2583 ± 0.0085	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
4	GCN-SSM ★ proposed	-2.2446 ± 0.0027	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
5	DRew-GCN GNN baseline	-2.1004 ± 0.0256	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
6	DRew-GCN + delay GNN baseline	-2.0291 ± 0.0240	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
7	PH-DGN GNN baseline	-0.9348 ± 0.2097	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
8	SWAN GNN baseline	-0.0739 ± 0.2190	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
9	ADGN GNN baseline	0.4296 ± 0.1003	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
10	A-DGN GNN baseline	0.4296 ± 0.1003	—	Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling no code May 2025 May '25
11	GPS Hyb baseline	0.6077 ± 0.0282	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
12	GRAND GNN baseline	0.6602 ± 0.1393	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
13	GraphCON GNN baseline	0.6833 ± 0.0074	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
14	GCNII GNN baseline	0.7640 ± 0.0355	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
15	GraphSAGE GNN baseline	0.7863 ± 0.0207	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
16	GAT GNN baseline	0.7909 ± 0.0222	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
17	DGC GNN baseline	0.8261 ± 0.0032	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
18	GCN GNN ★ proposed	0.8468 ± 0.0028	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
19	GIN GNN baseline	0.9504 ± 0.0007	—	On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph … no code Feb 2025 Feb '25
20	SWAN GNN ✎ baseline	—	-0.0739	TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows no code Aug 2025 Aug '25
21	PH-DGN GNN ✎ baseline	—	-0.9348	TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows no code Aug 2025 Aug '25
22	TANGO-GatedGCN Hyb ✎ ★ proposed	—	-1.7419	TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows no code Aug 2025 Aug '25
23	TANGO-GPS Hyb ✎ ★ proposed	—	-2.1455	TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows no code Aug 2025 Aug '25

SOTA performance set a new SOTA at the time matched the SOTA at the time

Structure

Coverage