Papers › Edge Directionality Improves Learning on Heterophilic Graphs
Edge Directionality Improves Learning on Heterophilic Graphs
Emanuele Rossi, Bertrand Charpentier, Francesco Di Giovanni, Fabrizio Frasca, Stephan Günnemann, Michael Bronstein
Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making the graph undirected. The reasons for this are historical: 1) many early variants of spectral GNNs explicitly required undirected graphs, and 2) the first benchmarks on homophilic graphs did not find significant gain from using direction. In this paper, we show that in heterophilic settings, treating the graph as directed increases the effective homophily of the graph, suggesting a potential gain from the correct use of directionality information. To this end, we introduce Directed Graph Neural Network (Dir-GNN), a novel general framework for deep learning on directed graphs. Dir-GNN can be used to extend any Message Passing Neural Network (MPNN) to account for edge directionality information by performing separate aggregations of the incoming and outgoing edges. We prove that Dir-GNN matches the expressivity of the Directed Weisfeiler-Lehman test, exceeding that of conventional MPNNs. In extensive experiments, we validate that while our framework leaves performance unchanged on homophilic datasets, it leads to large gains over base models such as GCN, GAT and GraphSage on heterophilic benchmarks, outperforming much more complex methods and achieving new state-of-the-art results.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2305.10498")
Code
Syntology Ran 3 of 5 code samples harvested from 1 repository linked to this paper; 2 have no recorded run. Of those that ran: 3 ran with no contract checked.
By repository: official repository: 5 samples from 1 repository, 3 ran. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
5 samples harvested; 3 ran; 0 honoured the contract we drafted; 2 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 0 of the 5 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from emalgorithm/directed-graph-neural-network. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.
Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.
aa7b67adc8e742a7 · report
3c3affd0e729d7f6 · report
921807f811fcb94a · report
1b4e100d3857a49a · report
7c6099619413280b · report
Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Node Classification | Chameleon | Dir-GNN | Accuracy | 79.71±1.26 | #3 of 61 | Archive leaderboard | report |
| Node Classification | Squirrel | Dir-GNN | Accuracy | 75.31±1.92 | #3 of 59 | Archive leaderboard | report |
| Node Classification | arXiv-year | Dir-GNN | Accuracy | 64.08±0.26 | #3 of 12 | Archive leaderboard | report |
| Node Classification on Non-Homophilic (Heterophilic) Graphs | Chameleon (48%/32%/20% fixed splits) | Dir-GNN | 1:1 Accuracy | 79.71±1.26 | #2 of 29 | Archive leaderboard | report |
| Node Classification on Non-Homophilic (Heterophilic) Graphs | Squirrel (48%/32%/20% fixed splits) | Dir-GNN | 1:1 Accuracy | 75.31±1.92 | #2 of 29 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections