When Connected Does Not Mean Similar: Charting the Homophily Boundary of SNAP-KG for Streaming Entity Integration

# When Connected Does Not Mean Similar: Charting the Homophily Boundary of SNAP-KG for Streaming Entity Integration
Source: [https://arxiv.org/html/2609.12356](https://arxiv.org/html/2609.12356)
###### Abstract

SNAP\-KG is a framework for assigning newly arriving entities to semantic communities in a growing knowledge graph \(KG\) using only their raw features, with no graph access and no retraining at inference time\. It was evaluated on five multi\-view benchmarks and a 2\.4M\-node OGB\-WikiKG2 KG\. In each of these datasets, at least one graph view is*homophilous*, meaning that connected nodes usually belong to the same class, and SNAP\-KG performs well on all of them\. This paper asks what happens outside that setting\. We extend the evaluation to three heterophilous graphs \(Texas, Wisconsin, Chameleon\) and measure the edge homophily of every view\. When no homophilous view is available, clustering quality drops sharply for both SNAP\-KG and the transductive baselines used in its original evaluation\. What decides this is the homophily of the relation, not the number of relations\. Multi\-view fusion still helps, but only when at least one homophilous relation provides a reliable foundation\. The homophily assumption is therefore shared by the whole method family, not specific to SNAP\-KG\. We argue that heterophilous multi\-view clustering is a separate research problem, outside the scope of this work\. As future work, we outline how a heterophily\-aware teacher could be distilled into SNAP\-KG’s projector to serve both homophilous and heterophilous KGs\.

###### keywords

Knowledge Graph Construction ,Multi\-View Graph Clustering ,Graph Heterophily ,Streaming Entity Integration ,Inductive Learning

††copyrightyear:2026††copyright:Copyright for this paper by its authors\. Use permitted under Creative Commons License Attribution 4\.0 International \(CC BY 4\.0\)\.††venue:ISWC 2026 Companion Volume, October 25–29, 2026, Bari, Italy††email:linj26@rpi\.edu††email:senevo@rpi\.edu††address:Rensselaer Polytechnic Institute, Troy, NY 12180, USA## 1Introduction

KG construction pipelines must keep integrating newly arriving entities into a growing graph\. A new entity arrives with no graph connectivity: it emerges from the upstream acquisition phase as a raw feature vector, and it must be placed into a semantic community before entity resolution \(ER\) and link prediction \(LP\) can run over a small candidate set instead of the entire node population\. Multi\-view graph clustering methods build high\-quality, relationally informed communities by treating each KG relation type as a separate structural view, but they are transductive: they cannot place unseen entities without retraining[Pan and Kang \(2021\)](https://arxiv.org/html/2609.12356#bib.bib10)\. Streaming Node Assignment via Projection for KG Entity Integration \(SNAP\-KG\)[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)closes this gap\. SNAP\-KG distills a multi\-view Graph Neural Network \(GNN\) and Transformer encoder into a lightweight Multi\-Layer Perceptron \(MLP\) projectorfϕf\_\{\\phi\}[Zhang et al\. \(2021\)](https://arxiv.org/html/2609.12356#bib.bib9)\. At inference, any new entity is embedded from its raw features alone and assigned to the nearest cluster centroid, with no graph access and no retraining\. On five multi\-view benchmarks and a 2\.4M\-node OGB\-WikiKG2 KG[Hu et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib15), this matches the quality of full retraining at an order\-of\-magnitude lower cost\.

SNAP\-KG depends on one structural assumption:*connected nodes tend to be similar*, a property known as homophily[Zhu et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib5)\. All five benchmarks used to evaluate SNAP\-KG satisfy this property\. This raises a natural question: what happens when it does not hold?

### Contribution\.

This paper extends the evaluation of SNAP\-KG in four ways:\(i\)new clustering experiments on three standard heterophilous graphs, where connected nodes tend to belong to*different*classes \(Texas, Wisconsin, Chameleon\)[Pei et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib6);[Rozemberczki et al\. \(2021\)](https://arxiv.org/html/2609.12356#bib.bib7), run over five seeds;\(ii\)a measurement of per\-view edge homophily for all eight evaluated datasets, which links SNAP\-KG’s clustering quality to a graph property that can be checked before deployment, together with a single\-view comparison that separates heterophily from the number of views;\(iii\)evidence that the transductive baselines from the paper’s evaluation drop in the same way, set against the dedicated heterophilous\-clustering literature; and\(iv\)a concrete research roadmap for extending streaming entity integration to heterophilous KGs\.

## 2SNAP\-KG and Its Homophily Assumption

![Refer to caption](https://arxiv.org/html/2609.12356v1/pipeline.png)Figure 1:The SNAP\-KG framework[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)\. Adaptive graph preprocessing, view\-specific GNNs, and a multi\-view encoder produce unified embeddings during training; the projectorfϕf\_\{\\phi\}is distilled to reproduce them from raw features and is the only component used for streaming inference\.Figure[1](https://arxiv.org/html/2609.12356#S2.F1)summarizes the framework\. Homophily enters it in three places\. First,*adaptive graph preprocessing*ranks each node’s neighbors by feature cosine similarity and keeps only the most similar ones; under heterophily, the useful neighbors are the dissimilar ones[Zhu et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib5), so this step throws away the structural signal\. Second, the*contrastive objective*treats a node’s kept neighbors as its positives and pulls their embeddings together; under heterophily, this pulls nodes of different classes into the same region of the embedding space\. Third, the*projector*is distilled from those embeddings, so it inherits both effects: whatever the teacher mixes together, the student cannot pull apart\. None of this is specific to SNAP\-KG\. It is the normal behavior of graph encoders that assume homophily[Zhu et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib5), and Section[3](https://arxiv.org/html/2609.12356#S3)shows that the transductive baselines exhibit the same performance drop\.

## 3A Scope Study on Heterophilous Graphs

### Setup\.

We evaluate on three graphs that are standard hard cases in the heterophily literature:TexasandWisconsin, webpage networks from the WebKB collection[Pei et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib6), andChameleon, a Wikipedia page\-link network[Rozemberczki et al\. \(2021\)](https://arxiv.org/html/2609.12356#bib.bib7)whose five classes come from binning the page\-traffic target\. Each of these graphs is defined by a single relation, so SNAP\-KG operates on that one view\. This raises an obvious question: is the drop caused by heterophily, or simply by using one view instead of several? Table[2](https://arxiv.org/html/2609.12356#S3.T2)separates the two\. All runs use SNAP\-KG’s original settings, repeated using five random seeds\. We report clustering accuracy \(ACC\) and normalized mutual information \(NMI\); across seeds, the standard deviation of ACC stays below 3\.7 points\. For every dataset in this study, including those previously used to evaluate SNAP\-KG, we also report*edge homophily*, the fraction of edges whose two endpoints share a class label[Zhu et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib5), computed per view on the raw graphs before adaptive filtering\.

Table 1:Edge homophily and SNAP\-KG clustering quality across all eight evaluated datasets\.hmaxh\_\{\\max\}/hmeanh\_\{\\mathrm\{mean\}\}: highest / mean edge homophily across views\. Upper block: benchmarks previously used to evaluate SNAP\-KG[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)\. Lower block: new heterophilous results \(mean over five random seeds\)\. The heterophilous graphs are single\-relation and are run in SNAP\-KG’s single\-view configuration\.DatasetNodesViewshmaxh\_\{\\max\}hmeanh\_\{\\mathrm\{mean\}\}ACC \(%\)NMI \(%\)ACM3,02520\.820\.7391\.5071\.08DBLP4,05730\.800\.6091\.8274\.03IMDB4,78020\.620\.5546\.673\.42YELP2,61430\.640\.4991\.2069\.65MAG113,91920\.660\.6668\.2050\.85Texas18310\.060\.0636\.618\.08Wisconsin25110\.180\.1835\.149\.72Chameleon2,27710\.320\.3231\.078\.80
### Quality is associated with the availability of a homophilous view\.

Table[1](https://arxiv.org/html/2609.12356#S3.T1)places the new results next to the benchmarks previously used to evaluate SNAP\-KG[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)\. The pattern is clear, though it is a correlation rather than proof of cause; Section[2](https://arxiv.org/html/2609.12356#S2)gives the mechanism\. Every dataset on which SNAP\-KG achieves more than 90% ACC has at least one view with edge homophily of 0\.64 or higher; MAG, athmax=0\.66h\_\{\\max\}\{=\}0\.66, with four classes, and a much larger scale, still reaches 68\.20%\. The three heterophilous graphs have no view above 0\.32 in terms of*edge homophily*, and quality falls sharply: ACC drops to 36\.61% on Texas, 35\.14% on Wisconsin, and 31\.07% on Chameleon, with NMI in the single digits\. IMDB shows that a moderately homophilous view is not enough on its own: prior SNAP\-KG results show that its views carry little signal that separates the classes for any method[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)\. The heterophilous graphs show the opposite problem: no view is homophilous at all, so multi\-view fusion has nothing reliable to build on\. A KG with several genuinely distinct heterophilous relations would also stress the fusion stage; standard heterophily benchmarks do not provide a KG with several distinct heterophilous relations, so we leave that case to future work\.

Table 2:One homophilous and one heterophilous relation of DBLP and YELP, each used on its own, from the original SNAP\-KG single\-view ablation[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)\. Every row uses a single view, so the number of views is fixed and only the relation changes\.DatasetRelation usedhhACC \(%\)NMI \(%\)DBLPAPVPA0\.6790\.0771\.12DBLPAPTPA0\.3256\.4221\.51YELPBSB0\.6490\.0566\.58YELPBUB0\.4537\.180\.57
### Heterophily, not the number of views\.

Table[2](https://arxiv.org/html/2609.12356#S3.T2)fixes the number of views at one and lets only the relation change, using results from the SNAP\-KG single\-view ablation[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)\. One homophilous relation is already enough: APVPA alone yields DBLP 90\.07% ACC against 91\.82% for the full three\-view model, while BSB alone yields YELP 90\.05% against 91\.20%\. Heterophilous relations perform substantially worse: APTPA alone yields 56\.42% ACC on DBLP, while BUB alone yields 37\.18% on YELP, close to the 31\.07–36\.61% range observed on Texas, Wisconsin, and Chameleon\. The drop therefore follows the homophily of the relation, not the number of relations\.

Table 3:Clustering on the heterophilous graphs: SNAP\-KG versus transductive clustering baselines previously used to evaluate SNAP\-KG\.TexasWisconsinChameleonMethodACC \(%\)NMI \(%\)ACC \(%\)NMI \(%\)ACC \(%\)NMI \(%\)AGE[Cui et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib11)33\.996\.1433\.5510\.4736\.6810\.59O2MAC[Fan et al\. \(2020\)](https://arxiv.org/html/2609.12356#bib.bib12)49\.184\.1045\.825\.6732\.158\.95BMGC[Shen et al\. \(2024\)](https://arxiv.org/html/2609.12356#bib.bib14)36\.507\.8842\.4814\.9931\.8610\.64DuaLGR[Ling et al\. \(2023\)](https://arxiv.org/html/2609.12356#bib.bib13)55\.7432\.1358\.5742\.0741\.2418\.22SNAP\-KG \(ours\)36\.618\.0835\.149\.7231\.078\.80
### The limitation is shared, not specific\.

Table[3](https://arxiv.org/html/2609.12356#S3.T3)reports the transductive baselines from the accompanying paper’s evaluation on the same three graphs\. Methods that reach 82–93% ACC on ACM and DBLP[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)drop to 32–59% here\. DuaLGR drops the least, yet its best result, 58\.57% ACC on Wisconsin, still trails the three benchmarks above 90% by more than 30 points\. Although SNAP\-KG experiences a similar performance loss, it is the only method in the table that can assign streaming entities inductively, without retraining\. So the limitation belongs to the whole family of homophily\-assuming methods, transductive and inductive alike, and not to any single method in it\.

## 4Heterophilous Clustering Is a Different Problem

Supporting heterophilous graphs is more than a minor modification to SNAP\-KG; it is a research direction of its own[Gong et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib8)\. Recent work redesigns the representation itself: NGCE uses node features to guide encoding and combines homophilous and heterophilous patterns in multi\-view graph clustering[Ren et al\. \(2025\)](https://arxiv.org/html/2609.12356#bib.bib2); HeNCler learns an asymmetric similarity for node clustering in heterophilous graphs[Achten et al\. \(2025\)](https://arxiv.org/html/2609.12356#bib.bib3); SMHGC mines similarity to strengthen homophily for multi\-view heterophilous clustering[Chen et al\. \(2024\)](https://arxiv.org/html/2609.12356#bib.bib4)\. To the best of our knowledge, these methods all target the transductive setting\. This points to two independent axes\. SNAP\-KG provides*inductive, retraining\-free deployment*; the works above provide*heterophily\-aware representation*\. No current method offers both\. Combining them is a concrete opportunity, because SNAP\-KG’s distillation stage does not care how the teacher forms its embeddings: it only needs feature\-embedding pairs\. Replacing the homophily\-assuming GNN\-Transformer teacher with a heterophily\-aware multi\-view teacher, and distilling it into the same projectorfϕf\_\{\\phi\}, would extend streaming entity integration to heterophilous KGs without changing the deployment path\. Until then, practitioners can tell in advance whether SNAP\-KG is likely to work on a new KG by measuring the edge homophily of each relation, using a small labeled sample when one is available, or a feature\-similarity estimate if they do not\. If none of the relations is at least moderately homophilous, the resulting clusters should not be trusted\.

## 5Conclusion

This paper extends SNAP\-KG[Lin et al\. \(2026\)](https://arxiv.org/html/2609.12356#bib.bib1)with a scope study on heterophilous graphs\. New five\-seed SNAP\-KG experiments on Texas, Wisconsin, and Chameleon, together with a homophily measurement of all eight datasets, show that SNAP\-KG’s strong results go together with having at least one homophilous view, and that quality falls sharply when none is present, both for SNAP\-KG and for the transductive baselines\. A single\-view comparison shows that this depends on the homophily of the relation rather than on how many relations a dataset has\. This failure marks the boundary between two research problems: streaming inductive deployment, which SNAP\-KG solves, and heterophily\-aware representation, which a dedicated line of work addresses[Ren et al\. \(2025\)](https://arxiv.org/html/2609.12356#bib.bib2);[Achten et al\. \(2025\)](https://arxiv.org/html/2609.12356#bib.bib3);[Chen et al\. \(2024\)](https://arxiv.org/html/2609.12356#bib.bib4)\. Distilling a heterophily\-aware teacher into SNAP\-KG’s streaming projector is a concrete path to serving both settings, and is the next direction for this work\.

## Declaration on Generative AI

We used a large language model \(Claude, Anthropic\) solely to assist with grammar correction and writing refinement\. All ideas, problem formulation, methodology, experimental design, results, and conclusions are entirely our own\. We take full responsibility for the accuracy and integrity of all content presented in this work\.

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