Heterogeneous Graph Condensation via Role-Aware Clustering

# Heterogeneous Graph Condensation via Role-Aware Clustering
Source: [https://arxiv.org/html/2607.03097](https://arxiv.org/html/2607.03097)
###### Abstract

Heterogeneous Graph Neural Networks \(HGNNs\) have exhibited remarkable efficacy in modeling complex systems with multiple types of nodes and relations, yet their training on large\-scale heterogeneous graphs remains computationally prohibitive\. Although graph condensation methods can effectively improve learning efficiency on large\-scale graphs, existing condensation processes are mainly designed for homogeneous graphs and typically rely on computationally expensive gradient matching or bilevel optimization paradigms, rendering them impractical for heterogeneous settings\. To address these limitations, we propose HGC\-RC, a simple yet effective role\-aware heterogeneous graph condensation framework\. Specifically, HGC\-RC first extracts semantically enhanced node embeddings via lightweight propagation\. It then introduces a role\-aware hybrid clustering strategy consisting of class\-partitioned clustering for labeled target nodes to preserve class distributions and unsupervised type\-wise clustering for non\-target nodes to retain critical cross\-type connectivity\. Finally, a compact heterogeneous graph is efficiently reconstructed based on the resulting cluster assignments\. Extensive experiments demonstrate that HGC\-RC outperforms state\-of\-the\-art baselines, offering a practical pathway to accelerate HGNN training on large\-scale heterogeneous graphs without sacrificing task performance\.

## IINTRODUCTION

Heterogeneous graphs are widely used to model complex relational systems in real\-world scenarios, such as academic networks, recommender systems, and knowledge\-driven platforms\[[90](https://arxiv.org/html/2607.03097#bib.bib114),[58](https://arxiv.org/html/2607.03097#bib.bib124),[41](https://arxiv.org/html/2607.03097#bib.bib128),[29](https://arxiv.org/html/2607.03097#bib.bib129),[19](https://arxiv.org/html/2607.03097#bib.bib142),[55](https://arxiv.org/html/2607.03097#bib.bib150)\]\. Prior to the rise of heterogeneous models, standard Graph Neural Networks \(GNNs\)\[[34](https://arxiv.org/html/2607.03097#bib.bib1),[59](https://arxiv.org/html/2607.03097#bib.bib2),[21](https://arxiv.org/html/2607.03097#bib.bib19),[7](https://arxiv.org/html/2607.03097#bib.bib21),[96](https://arxiv.org/html/2607.03097#bib.bib24),[95](https://arxiv.org/html/2607.03097#bib.bib106),[24](https://arxiv.org/html/2607.03097#bib.bib123),[4](https://arxiv.org/html/2607.03097#bib.bib146),[38](https://arxiv.org/html/2607.03097#bib.bib151)\]demonstrated immense potential in homogeneous graph representation learning\. By explicitly characterizing multiple node and relation types, heterogeneous graphs provide richer semantics than homogeneous graphs\. To effectively model such heterogeneous interactions, heterogeneous graph neural networks \(HGNNs\)\[[64](https://arxiv.org/html/2607.03097#bib.bib102),[63](https://arxiv.org/html/2607.03097#bib.bib103),[25](https://arxiv.org/html/2607.03097#bib.bib120),[67](https://arxiv.org/html/2607.03097#bib.bib11),[97](https://arxiv.org/html/2607.03097#bib.bib44),[14](https://arxiv.org/html/2607.03097#bib.bib45),[27](https://arxiv.org/html/2607.03097#bib.bib43),[85](https://arxiv.org/html/2607.03097#bib.bib14),[62](https://arxiv.org/html/2607.03097#bib.bib108),[43](https://arxiv.org/html/2607.03097#bib.bib126),[84](https://arxiv.org/html/2607.03097#bib.bib135),[76](https://arxiv.org/html/2607.03097#bib.bib138),[1](https://arxiv.org/html/2607.03097#bib.bib152)\]have achieved strong performance in a variety of domains, including traffic networks\[[94](https://arxiv.org/html/2607.03097#bib.bib100),[53](https://arxiv.org/html/2607.03097#bib.bib117),[92](https://arxiv.org/html/2607.03097#bib.bib115),[80](https://arxiv.org/html/2607.03097#bib.bib130),[42](https://arxiv.org/html/2607.03097#bib.bib131),[78](https://arxiv.org/html/2607.03097#bib.bib137),[28](https://arxiv.org/html/2607.03097#bib.bib139),[9](https://arxiv.org/html/2607.03097#bib.bib149),[56](https://arxiv.org/html/2607.03097#bib.bib153)\], biology\[[3](https://arxiv.org/html/2607.03097#bib.bib121),[22](https://arxiv.org/html/2607.03097#bib.bib104),[35](https://arxiv.org/html/2607.03097#bib.bib134),[83](https://arxiv.org/html/2607.03097#bib.bib136),[13](https://arxiv.org/html/2607.03097#bib.bib141),[49](https://arxiv.org/html/2607.03097#bib.bib145),[73](https://arxiv.org/html/2607.03097#bib.bib127),[47](https://arxiv.org/html/2607.03097#bib.bib154)\], relational databases\[[75](https://arxiv.org/html/2607.03097#bib.bib118),[52](https://arxiv.org/html/2607.03097#bib.bib119),[36](https://arxiv.org/html/2607.03097#bib.bib101),[72](https://arxiv.org/html/2607.03097#bib.bib116),[89](https://arxiv.org/html/2607.03097#bib.bib111),[39](https://arxiv.org/html/2607.03097#bib.bib140),[71](https://arxiv.org/html/2607.03097#bib.bib148),[74](https://arxiv.org/html/2607.03097#bib.bib155)\], as well as emerging applications like event detection, link prediction, and disease prognosis\[[10](https://arxiv.org/html/2607.03097#bib.bib91),[102](https://arxiv.org/html/2607.03097#bib.bib92),[12](https://arxiv.org/html/2607.03097#bib.bib95),[99](https://arxiv.org/html/2607.03097#bib.bib96),[77](https://arxiv.org/html/2607.03097#bib.bib93),[98](https://arxiv.org/html/2607.03097#bib.bib94),[65](https://arxiv.org/html/2607.03097#bib.bib132),[26](https://arxiv.org/html/2607.03097#bib.bib147),[8](https://arxiv.org/html/2607.03097#bib.bib156)\]\. Despite their expressive power, training HGNNs on large heterogeneous graphs remains expensive due to repeated relation\-aware propagation, high\-dimensional semantic features, and neighborhood expansion\.

*Graph condensation*\(GC\), which constructs a compact graph while preserving downstream utility, has emerged as a promising paradigm for accelerating GNN training\[[33](https://arxiv.org/html/2607.03097#bib.bib53),[37](https://arxiv.org/html/2607.03097#bib.bib105),[87](https://arxiv.org/html/2607.03097#bib.bib109),[91](https://arxiv.org/html/2607.03097#bib.bib110),[51](https://arxiv.org/html/2607.03097#bib.bib125),[48](https://arxiv.org/html/2607.03097#bib.bib144),[54](https://arxiv.org/html/2607.03097#bib.bib157)\]\. Existing GC methods have achieved encouraging results on homogeneous graphs, where most approaches rely on gradient matching or bi\-level optimization to learn compact synthetic structures and features\[[93](https://arxiv.org/html/2607.03097#bib.bib112),[86](https://arxiv.org/html/2607.03097#bib.bib113),[79](https://arxiv.org/html/2607.03097#bib.bib133),[68](https://arxiv.org/html/2607.03097#bib.bib158)\]\. However, extending these methods to heterogeneous settings is far from straightforward\. In heterogeneous graphs, multiple feature spaces, relation semantics, and cross\-type dependencies must be preserved simultaneously, while naive homogenization, such as relation union or meta\-path projection, may distort relation semantics and class balance\. Although a few studies have begun to consider heterogeneous graph condensation, such as HGCond\[[15](https://arxiv.org/html/2607.03097#bib.bib73)\], these methods remain optimization\-heavy and sensitive to the relay model\.

A key challenge of heterogeneous graph condensation lies in the*role asymmetry*among node types\. Specifically, labeled*target\-type*nodes directly determine the downstream decision boundary, whereas*non\-target*nodes mainly provide semantic and structural support\. As illustrated in Figure[1](https://arxiv.org/html/2607.03097#S1.F1), applying a uniform condensation strategy may be suitable for homogeneous graphs, where nodes play relatively consistent roles\. In contrast, in heterogeneous graphs, treating all nodes equally during condensation may blur the class structure of target nodes and discard critical support nodes\. Therefore, capturing and exploiting node\-role differences is essential for effective heterogeneous graph condensation\.

![Refer to caption](https://arxiv.org/html/2607.03097v1/x1.png)Figure 1:Motivation of role\-aware condensation in heterogeneous graphs\. \(a\) Uniform condensation suits homogeneous graphs\. \(b\) In heterogeneous graphs, it may mix target classes and remove support nodes\.To address this issue, we proposeHGC\-RC, a role\-aware framework for heterogeneous graph condensation\. Instead of relying on expensive iterative synthetic graph optimization, HGC\-RC constructs a compact heterogeneous graph from a data\-centric perspective\. Specifically, HGC\-RC first computes semantic embeddings using SeHGNN preprocessing, then performs class\-partitioned clustering for target nodes and type\-wise unsupervised clustering for non\-target nodes\. Based on the resulting cluster assignments, it aggregates original node features and reconstructs a compact heterogeneous graph through inter\-cluster connectivity summarization\.

Our main contributions are as follows:

- •We formulate heterogeneous graph condensation from a*role\-aware*perspective, highlighting the asymmetric roles of target and non\-target nodes in preserving downstream classification utility\.
- •We proposeHGC\-RC, an efficient optimization\-free framework that combines class\-partitioned clustering for target nodes, type\-wise unsupervised clustering for non\-target nodes, and cluster\-level graph reconstruction\.
- •Experiments on three heterogeneous benchmarks show thatHGC\-RCachieves competitive performance under high compression with substantially lower condensation cost than representative optimization\-based baselines\.

## IIPRELIMINARIES

In this section, we introduce the notations, problem formulation, and background on graph condensation\.

### II\-ANotations and Problem Formulation

A heterogeneous graph is denoted as𝒢=\(𝒱,ℰ,ϕ,ψ\)\\mathcal\{G\}=\(\\mathcal\{V\},\\mathcal\{E\},\\phi,\\psi\), where𝒱\\mathcal\{V\}andℰ\\mathcal\{E\}are the node and edge sets, respectively\. The mappingϕ:𝒱→𝒯\\phi:\\mathcal\{V\}\\rightarrow\\mathcal\{T\}assigns each node to a node type, andψ:ℰ→ℛ\\psi:\\mathcal\{E\}\\rightarrow\\mathcal\{R\}assigns each edge to a relation type, where𝒯\\mathcal\{T\}andℛ\\mathcal\{R\}denote the sets of node types and relation types, respectively\. The graph is homogeneous when\|𝒯\|=\|ℛ\|=1\|\\mathcal\{T\}\|=\|\\mathcal\{R\}\|=1\.

We focus on a node classification task defined on a*target node type*τt∈𝒯\\tau\_\{t\}\\in\\mathcal\{T\}\(e\.g\.,Authorin DBLP\[[50](https://arxiv.org/html/2607.03097#bib.bib12)\]\), while the remaining node types act as*non\-target*types that provide semantic context and structural support\. Let

𝒱t=\{v∈𝒱∣ϕ​\(v\)=τt\}\\mathcal\{V\}\_\{t\}=\\\{v\\in\\mathcal\{V\}\\mid\\phi\(v\)=\\tau\_\{t\}\\\}\(1\)be the target\-type node set, and let

𝒱u=𝒱∖𝒱t\\mathcal\{V\}\_\{u\}=\\mathcal\{V\}\\setminus\\mathcal\{V\}\_\{t\}\(2\)be the non\-target node set\. Target nodes have features𝐗τt\\mathbf\{X\}\_\{\\tau\_\{t\}\}and labels𝐲∈\{1,…,C\}\|𝒱t\|\\mathbf\{y\}\\in\\\{1,\\dots,C\\\}^\{\|\\mathcal\{V\}\_\{t\}\|\}overCCclasses, whereas non\-target nodes have features\{𝐗τ\}τ∈𝒯∖\{τt\}\\\{\\mathbf\{X\}\_\{\\tau\}\\\}\_\{\\tau\\in\\mathcal\{T\}\\setminus\\\{\\tau\_\{t\}\\\}\}and no task labels\.

Meta\-path features\.Following common heterogeneous learning practice, we consider a set of meta\-paths𝒫\\mathcal\{P\}defined over node types\. A meta\-pathP∈𝒫P\\in\\mathcal\{P\}can be written as

P:τ1→τ2→⋯→τL\.P:\\tau\_\{1\}\\rightarrow\\tau\_\{2\}\\rightarrow\\cdots\\rightarrow\\tau\_\{L\}\.\(3\)For each target node, meta\-path\-based features can be constructed by propagating information alongPP, yielding𝐗P\\mathbf\{X\}^\{P\}\.

Problem definition\.Given the original heterogeneous graph𝒢\\mathcal\{G\}and a condensation ratioρ∈\(0,1\)\\rho\\in\(0,1\), our goal is to construct a condensed heterogeneous graph

𝒢c=\(𝒱c,\{𝐀rc\}r∈ℛ,𝐗c,𝐲c\),\\mathcal\{G\}\_\{c\}=\\big\(\\mathcal\{V\}\_\{c\},\\\{\\mathbf\{A\}\_\{r\}^\{c\}\\\}\_\{r\\in\\mathcal\{R\}\},\\mathbf\{X\}\_\{c\},\\mathbf\{y\}\_\{c\}\\big\),\(4\)with\|𝒱c\|≪\|𝒱\|\|\\mathcal\{V\}\_\{c\}\|\\ll\|\\mathcal\{V\}\|, such that an HGNN trained on𝒢c\\mathcal\{G\}\_\{c\}achieves performance comparable to that obtained on𝒢\\mathcal\{G\}\. We allocate a type\-wise condensation budget:

\|𝒱c\(τ\)\|=max⁡\(1,⌊ρ​\|𝒱\(τ\)\|⌋\),\|\\mathcal\{V\}\_\{c\}^\{\(\\tau\)\}\|=\\max\\left\(1,\\left\\lfloor\\rho\\,\|\\mathcal\{V\}^\{\(\\tau\)\}\|\\right\\rfloor\\right\),\(5\)where

𝒱\(τ\)=\{v∈𝒱∣ϕ​\(v\)=τ\}\\mathcal\{V\}^\{\(\\tau\)\}=\\\{v\\in\\mathcal\{V\}\\mid\\phi\(v\)=\\tau\\\}\(6\)is the node set of typeτ\\tau, and𝒱c\(τ\)\\mathcal\{V\}\_\{c\}^\{\(\\tau\)\}denotes the condensed nodes of typeτ\\tau\. For the target type, HGC\-RC further allocates the budget across classes withinℳ\\mathcal\{M\}to preserve class balance\. The condensed features𝐗c\\mathbf\{X\}\_\{c\}are obtained by aggregating original node features according to the cluster assignments learned in the embedding space\.

Formally, letfθf\_\{\\theta\}be an HGNN and letℒ\\mathcal\{L\}denote the task loss on target nodes\. Our goal is to construct a condensed graph such that training an HGNN on𝒢c\\mathcal\{G\}\_\{c\}preserves the downstream utility of training on the original graph𝒢\\mathcal\{G\}under the same task, while satisfying the budget controlled byρ\\rho\. In practice,𝒢c\\mathcal\{G\}\_\{c\}serves as a compact*training graph*\. The condensation maskℳ\\mathcal\{M\}corresponds to the labeled training target nodes to be condensed, while validation and test target nodes remain on the original graph for downstream evaluation\. Therefore, the objective of condensation is to preserve the training utility of the original heterogeneous graph under a strict node budget without changing the standard evaluation protocol\.

### II\-BGraph Reduction

Graph reduction aims to reduce graph size while preserving downstream GNN utility\. Existing methods mainly fall into three categories:*graph sparsification*,*graph coarsening*, and*graph condensation*\[[23](https://arxiv.org/html/2607.03097#bib.bib79),[88](https://arxiv.org/html/2607.03097#bib.bib107),[44](https://arxiv.org/html/2607.03097#bib.bib143),[31](https://arxiv.org/html/2607.03097#bib.bib159)\]\.

Graph Sparsification & Coarsening\.Graph sparsification selects a subset of nodes or edges to approximately preserve the original graph quality\[[57](https://arxiv.org/html/2607.03097#bib.bib62),[2](https://arxiv.org/html/2607.03097#bib.bib122)\]\. Representative coreset\-based methods include Herding\[[69](https://arxiv.org/html/2607.03097#bib.bib69)\]and K\-center\[[70](https://arxiv.org/html/2607.03097#bib.bib70)\], which select representative samples in the feature space\. In heterogeneous graphs, sparsification is more challenging because node/edge types and meta\-path semantics must be preserved; naive sampling may distort relation distributions and class balance, causing notable accuracy drops at low keep ratios\[[11](https://arxiv.org/html/2607.03097#bib.bib64)\]\. Graph coarsening groups original nodes into super\-nodes and defines their connections to preserve structural information\[[30](https://arxiv.org/html/2607.03097#bib.bib80)\]\. However, under high compression, sparsification and coarsening may lose critical semantics and are often too topology\-centered to reliably support heterogeneous downstream tasks\.

Graph Condensation\.Graph condensation \(GC\) compresses a large graph into a much smaller*synthetic*graph while preserving training utility, inspired by the success of dataset distillation in computer vision\[[6](https://arxiv.org/html/2607.03097#bib.bib58),[66](https://arxiv.org/html/2607.03097#bib.bib59),[100](https://arxiv.org/html/2607.03097#bib.bib61)\]\. A representative early method, GCond\[[33](https://arxiv.org/html/2607.03097#bib.bib53)\], formulates GC as a bi\-level optimization problem that matches gradients between the original and synthetic graphs to jointly learn condensed features and structure\. Subsequent methods improve efficiency by avoiding costly inner\-loop optimization and modeling discrete graph structures probabilistically\[[32](https://arxiv.org/html/2607.03097#bib.bib54)\]\. Other directions include trajectory\-based methods, structure\-free condensation such as SFGC\[[101](https://arxiv.org/html/2607.03097#bib.bib55)\], spectrum\-oriented regularization such as eigenbasis matching\[[46](https://arxiv.org/html/2607.03097#bib.bib57),[81](https://arxiv.org/html/2607.03097#bib.bib74)\], and distribution matching techniques\[[45](https://arxiv.org/html/2607.03097#bib.bib56)\]\. More recent GC methods further improve efficiency through precomputed features, simplified optimization, and lower construction cost\[[16](https://arxiv.org/html/2607.03097#bib.bib88),[17](https://arxiv.org/html/2607.03097#bib.bib89),[18](https://arxiv.org/html/2607.03097#bib.bib90),[20](https://arxiv.org/html/2607.03097#bib.bib98),[61](https://arxiv.org/html/2607.03097#bib.bib99),[60](https://arxiv.org/html/2607.03097#bib.bib160)\], among which GCPA\[[40](https://arxiv.org/html/2607.03097#bib.bib97)\]is representative\. Nevertheless, most GC methods remain optimization\-intensive and are mainly designed for homogeneous graphs\.

![Refer to caption](https://arxiv.org/html/2607.03097v1/framework.png)

Figure 2:The workflow of HGC\-RC\.Heterogeneous Graph Condensation\.Extending GC to heterogeneous graphs is non\-trivial due to multi\-type feature spaces, relation\-specific dependencies, and the need to preserve heterogeneous semantics\. HGCond\[[15](https://arxiv.org/html/2607.03097#bib.bib73)\]is among the first methods for this setting; it leverages clustering for initialization and adopts an orthogonal parameter sequence strategy to improve optimization stability\. However, it still relies on optimization\-driven condensation and is sensitive to the relay model and budget settings\. Graph\-Skeleton\[[5](https://arxiv.org/html/2607.03097#bib.bib78)\]also considers heterogeneous graphs, but condenses only background nodes while keeping all target nodes, which differs from general settings that compress both target and non\-target parts\.

## IIIFRAMEWORK

In this section, we presentHGC\-RC, a role\-aware framework for heterogeneous graph condensation\. As shown in Figure[2](https://arxiv.org/html/2607.03097#S2.F2), HGC\-RC consists of semantic embedding extraction, role\-aware clustering, and cluster\-level graph reconstruction, aiming to preserve discriminative target information and structural\-semantic support in a compact training graph\.

### III\-ASemantic\-Enhanced Embedding Generation

Given𝒢=\(𝒱,ℰ,ϕ,ψ\)\\mathcal\{G\}=\(\\mathcal\{V\},\\mathcal\{E\},\\phi,\\psi\)and a set of meta\-paths𝒫\\mathcal\{P\}, HGC\-RC first computes semantic\-enhanced embeddings for all nodes to provide a unified representation space for condensation\. Specifically, for each meta\-pathP∈𝒫P\\in\\mathcal\{P\}, we construct meta\-path features for target nodes by propagating information alongPP, yielding𝐗P\\mathbf\{X\}^\{P\}\.

Let𝐙∈ℝ\|𝒱\|×d\\mathbf\{Z\}\\in\\mathbb\{R\}^\{\|\\mathcal\{V\}\|\\times d\}denote the embedding matrix, where the row vector𝐳v\\mathbf\{z\}\_\{v\}corresponds to nodevv\. We write the embedding extraction stage as

𝐙=g​\(𝒢,\{𝐗P\}P∈𝒫\),\\mathbf\{Z\}=g\\Big\(\\mathcal\{G\},\\\{\\mathbf\{X\}^\{P\}\\\}\_\{P\\in\\mathcal\{P\}\}\\Big\),\(7\)whereg​\(⋅\)g\(\\cdot\)is instantiated by a SeHGNN\[[82](https://arxiv.org/html/2607.03097#bib.bib15)\]preprocessing encoder to capture multi\-relational semantics with low overhead\. The resulting embeddings encode both structural context and semantic patterns induced by meta\-paths, and serve as the unified input to the subsequent role\-aware hybrid clustering stage\.

### III\-BRole\-aware Hybrid Clustering

HGC\-RC performs role\-aware hybrid clustering in the embedding space𝐙\\mathbf\{Z\}\. The key idea is that*target nodes*should preserve class\-discriminative structure, while*non\-target nodes*should preserve structural support and cross\-type connectivity\. Accordingly, HGC\-RC applies class\-partitioned clustering to target nodes and unsupervised type\-wise clustering to non\-target nodes, thereby obtaining a mapping from original nodes to condensed clusters\.

Target nodes: class\-partitioned clustering\.Letℳ⊆𝒱t\\mathcal\{M\}\\subseteq\\mathcal\{V\}\_\{t\}denote the condensation mask \(typically the labeled training target nodes\), and labels𝐲\\mathbf\{y\}are only used withinℳ\\mathcal\{M\}\. Given ratioρ\\rho, we allocate the target\-type budget

Kt=max⁡\(1,⌊ρ​\|ℳ\|⌋\)\.K\_\{t\}=\\max\\Big\(1,\\big\\lfloor\\rho\\,\|\\mathcal\{M\}\|\\big\\rfloor\\Big\)\.\(8\)To preserve class balance, we further distributeKtK\_\{t\}across classes according to the label distribution inℳ\\mathcal\{M\}\. For classc∈\{1,…,C\}c\\in\\\{1,\\dots,C\\\}, let

ℳc=\{v∈ℳ∣yv=c\},\\mathcal\{M\}\_\{c\}=\\\{v\\in\\mathcal\{M\}\\mid y\_\{v\}=c\\\},\(9\)whereyvy\_\{v\}denotes the label of nodevv\. We allocate

kc=max⁡\(1,⌊Kt⋅\|ℳc\|\|ℳ\|⌋\),and adjust​∑c=1Ckc=Kt\.k\_\{c\}=\\max\\Big\(1,\\Big\\lfloor K\_\{t\}\\cdot\\frac\{\|\\mathcal\{M\}\_\{c\}\|\}\{\|\\mathcal\{M\}\|\}\\Big\\rfloor\\Big\),\\quad\\text\{and adjust \}\\sum\_\{c=1\}^\{C\}k\_\{c\}=K\_\{t\}\.\(10\)We then cluster embeddings within each class:

\{𝒞c,1,…,𝒞c,kc\}=Cluster​\(\{𝐳v\}v∈ℳc;kc\),\\\{\\mathcal\{C\}\_\{c,1\},\\dots,\\mathcal\{C\}\_\{c,k\_\{c\}\}\\\}=\\mathrm\{Cluster\}\\Big\(\\\{\\mathbf\{z\}\_\{v\}\\\}\_\{v\\in\\mathcal\{M\}\_\{c\}\};\\,k\_\{c\}\\Big\),\(11\)whereCluster​\(⋅\)\\mathrm\{Cluster\}\(\\cdot\)is instantiated by spectral clustering or k\-means\. This defines a mapping from target nodes inℳ\\mathcal\{M\}to condensed target clusters\. Nodes outsideℳ\\mathcal\{M\}do not participate in target\-node condensation\. Since target\-node clustering is performed in a class\-partitioned manner, each condensed target cluster is assigned the corresponding class labelcc\.

Non\-target nodes: unsupervised clustering\.For each non\-target typeτ∈𝒯∖\{τt\}\\tau\\in\\mathcal\{T\}\\setminus\\\{\\tau\_\{t\}\\\}, let

𝒱\(τ\)=\{v∈𝒱∣ϕ​\(v\)=τ\}\.\\mathcal\{V\}^\{\(\\tau\)\}=\\\{v\\in\\mathcal\{V\}\\mid\\phi\(v\)=\\tau\\\}\.\(12\)We allocate a type\-wise budget consistent with the problem formulation:

Kτ=max⁡\(1,⌊ρ​\|𝒱\(τ\)\|⌋\)\.K\_\{\\tau\}=\\max\\Big\(1,\\big\\lfloor\\rho\\,\|\\mathcal\{V\}^\{\(\\tau\)\}\|\\big\\rfloor\\Big\)\.\(13\)We then cluster embeddings of this type without using labels:

\{𝒞τ,1,…,𝒞τ,Kτ\}=Cluster​\(\{𝐳v\}v∈𝒱\(τ\);Kτ\),\\\{\\mathcal\{C\}\_\{\\tau,1\},\\dots,\\mathcal\{C\}\_\{\\tau,K\_\{\\tau\}\}\\\}=\\mathrm\{Cluster\}\\Big\(\\\{\\mathbf\{z\}\_\{v\}\\\}\_\{v\\in\\mathcal\{V\}^\{\(\\tau\)\}\};\\,K\_\{\\tau\}\\Big\),\(14\)thereby defining a mapping from original non\-target nodes to condensed non\-target clusters\. These clusters preserve structural support and cross\-type semantic context for downstream learning\.

Finally, the condensed node set is written as

𝒱c=𝒱c\(t\)∪𝒱c\(u\),\\mathcal\{V\}\_\{c\}=\\mathcal\{V\}\_\{c\}^\{\(t\)\}\\cup\\mathcal\{V\}\_\{c\}^\{\(u\)\},\(15\)where𝒱c\(t\)\\mathcal\{V\}\_\{c\}^\{\(t\)\}consists of all condensed clusters obtained from target nodes inℳ\\mathcal\{M\}, and𝒱c\(u\)\\mathcal\{V\}\_\{c\}^\{\(u\)\}consists of all condensed clusters obtained from non\-target node types\. By construction,𝐲c\\mathbf\{y\}\_\{c\}is defined only on𝒱c\(t\)\\mathcal\{V\}\_\{c\}^\{\(t\)\}, while non\-target condensed nodes have no task labels\.

### III\-CCondensed Graph Reconstruction

Lets​\(v\)s\(v\)denote the cluster assignment of nodevv\. Based on the resulting assignments, HGC\-RC reconstructs a condensed heterogeneous graph by aggregating node features and summarizing inter\-cluster connectivity\.

Condensed feature construction\.Let𝐱v\\mathbf\{x\}\_\{v\}denote the original feature of nodevv, and let

𝒞k=\{v∣s​\(v\)=k\}\\mathcal\{C\}\_\{k\}=\\\{v\\mid s\(v\)=k\\\}\(16\)be the set of nodes assigned to condensed clusterkk\. The condensed feature is computed by

𝐱kc=1\|𝒞k\|​∑v∈𝒞k𝐱v\.\\mathbf\{x\}^\{c\}\_\{k\}=\\frac\{1\}\{\|\\mathcal\{C\}\_\{k\}\|\}\\sum\_\{v\\in\\mathcal\{C\}\_\{k\}\}\\mathbf\{x\}\_\{v\}\.\(17\)For target nodes, only nodes in the condensation mask participate in feature aggregation\.

Condensed label construction\.Labels are defined only for condensed target clusters, each of which inherits the corresponding class label\.

Condensed adjacency construction\.For each relation typer∈ℛr\\in\\mathcal\{R\}, let

ℰr=\{e=\(u,v\)∈ℰ∣ψ​\(e\)=r\}\\mathcal\{E\}\_\{r\}=\\\{e=\(u,v\)\\in\\mathcal\{E\}\\mid\\psi\(e\)=r\\\}\(18\)denote the edge set of relationrr\. We first compute the inter\-cluster edge count matrix:

Wrc​\(i,j\)=∑\(u,v\)∈ℰr𝟏​\[s​\(u\)=i,s​\(v\)=j\]\.W\_\{r\}^\{c\}\(i,j\)=\\sum\_\{\(u,v\)\\in\\mathcal\{E\}\_\{r\}\}\\mathbf\{1\}\[s\(u\)=i,\\ s\(v\)=j\]\.\(19\)To reduce cluster\-size bias, we normalize it as

W~rc​\(i,j\)=Wrc​\(i,j\)\|𝒞i\|​\|𝒞j\|\+ϵ,\\widetilde\{W\}\_\{r\}^\{c\}\(i,j\)=\\frac\{W\_\{r\}^\{c\}\(i,j\)\}\{\|\\mathcal\{C\}\_\{i\}\|\\,\|\\mathcal\{C\}\_\{j\}\|\+\\epsilon\},\(20\)whereϵ\\epsilonis a small constant\. We then compute a bounded edge score:

Src​\(i,j\)=σ​\(α​\(W~rc​\(i,j\)−βr\)\),S\_\{r\}^\{c\}\(i,j\)=\\sigma\\\!\\left\(\\alpha\\big\(\\widetilde\{W\}\_\{r\}^\{c\}\(i,j\)\-\\beta\_\{r\}\\big\)\\right\),\(21\)whereσ​\(⋅\)\\sigma\(\\cdot\)is the sigmoid function,α\\alphacontrols the sharpness, andβr\\beta\_\{r\}is a relation\-specific threshold\. The condensed adjacency is defined as

Arc​\(i,j\)=𝟏​\[Src​\(i,j\)\>δ\],A\_\{r\}^\{c\}\(i,j\)=\\mathbf\{1\}\\\!\\left\[S\_\{r\}^\{c\}\(i,j\)\>\\delta\\right\],\(22\)whereδ\\deltais a filtering threshold\. In our implementation,α=10\\alpha=10,δ=0\.5\\delta=0\.5, andβr\\beta\_\{r\}is set as the mean of nonzeroW~rc​\(i,j\)\\widetilde\{W\}\_\{r\}^\{c\}\(i,j\)values for relationrr\. The condensed graph is written as

𝒢c=\(𝒱c,\{𝐀rc\}r∈ℛ,𝐗c,𝐲c\)\.\\mathcal\{G\}\_\{c\}=\\Big\(\\mathcal\{V\}\_\{c\},\\\{\\mathbf\{A\}\_\{r\}^\{c\}\\\}\_\{r\\in\\mathcal\{R\}\},\\mathbf\{X\}\_\{c\},\\mathbf\{y\}\_\{c\}\\Big\)\.\(23\)
TABLE I:Experiment results of node classification prediction tasks on three datasets\.BaselinesProposedDatasetRatio \(r\)Random\-HGK\-Center\-HGCoarsening\-HGGCondGCPAHGCondHGC\-RCWhole DatasetACM1\.2%54\.21±1\.9254\.21\\pm 1\.9263\.54±1\.7363\.54\\pm 1\.7363\.29±2\.0563\.29\\pm 2\.0541\.78±8\.6241\.78\\pm 8\.6268\.62±0\.4168\.62\\pm 0\.4187\.41±1\.9887\.41\\pm 1\.9890\.76±0\.38\\boldsymbol\{90\.76\\pm 0\.38\}94\.18±0\.1494\.18\\pm 0\.142\.4%60\.12±2\.1160\.12\\pm 2\.1166\.23±1\.6766\.23\\pm 1\.6764\.69±1\.8864\.69\\pm 1\.8848\.59±6\.2848\.59\\pm 6\.2869\.71±0\.5269\.71\\pm 0\.5288\.21±2\.0288\.21\\pm 2\.0291\.26±0\.68\\boldsymbol\{91\.26\\pm 0\.68\}4\.8%60\.87±1\.7960\.87\\pm 1\.7968\.72±2\.1468\.72\\pm 2\.1469\.53±1\.6669\.53\\pm 1\.6650\.25±4\.5650\.25\\pm 4\.5669\.73±0\.4669\.73\\pm 0\.4684\.35±1\.9084\.35\\pm 1\.9091\.74±0\.40\\boldsymbol\{91\.74\\pm 0\.40\}9\.6%65\.41±1\.7465\.41\\pm 1\.7476\.54±2\.1876\.54\\pm 2\.1871\.88±1\.8271\.88\\pm 1\.8245\.36±6\.3245\.36\\pm 6\.3268\.61±0\.3968\.61\\pm 0\.3984\.21±1\.6984\.21\\pm 1\.6993\.46±0\.23\\boldsymbol\{93\.46\\pm 0\.23\}DBLP1\.2%39\.65±2\.0739\.65\\pm 2\.0760\.41±1\.9560\.41\\pm 1\.9554\.33±1\.7154\.33\\pm 1\.7153\.49±5\.5453\.49\\pm 5\.5476\.41±0\.8876\.41\\pm 0\.8892\.34±1\.88\\boldsymbol\{92\.34\\pm 1\.88\}88\.94±0\.68¯\\underline\{88\.94\\pm 0\.68\}95\.18±0\.1895\.18\\pm 0\.182\.4%49\.58±1\.8349\.58\\pm 1\.8364\.92±2\.0664\.92\\pm 2\.0658\.71±1\.6458\.71\\pm 1\.6444\.95±4\.2744\.95\\pm 4\.2775\.17±0\.9675\.17\\pm 0\.9693\.86±2\.12\\boldsymbol\{93\.86\\pm 2\.12\}89\.92±1\.07¯\\underline\{89\.92\\pm 1\.07\}4\.8%44\.63±1\.7644\.63\\pm 1\.7671\.54±2\.1971\.54\\pm 2\.1965\.33±1\.9765\.33\\pm 1\.9752\.95±9\.2352\.95\\pm 9\.2376\.24±0\.8376\.24\\pm 0\.8391\.62±1\.81¯\\underline\{91\.62\\pm 1\.81\}91\.70±0\.69\\boldsymbol\{91\.70\\pm 0\.69\}9\.6%56\.93±2\.1556\.93\\pm 2\.1578\.74±1\.6978\.74\\pm 1\.6977\.66±2\.0277\.66\\pm 2\.0246\.23±8\.2546\.23\\pm 8\.2575\.79±0\.7975\.79\\pm 0\.7991\.47±1\.75¯\\underline\{91\.47\\pm 1\.75\}92\.79±0\.36\\boldsymbol\{92\.79\\pm 0\.36\}IMDB1\.2%40\.16±1\.8740\.16\\pm 1\.8742\.71±2\.1042\.71\\pm 2\.1041\.26±1\.7841\.26\\pm 1\.7842\.12±6\.5742\.12\\pm 6\.5734\.52±0\.3134\.52\\pm 0\.3156\.54±1\.9356\.54\\pm 1\.9360\.14±0\.42\\boldsymbol\{60\.14\\pm 0\.42\}69\.84±0\.2469\.84\\pm 0\.242\.4%41\.69±2\.1741\.69\\pm 2\.1750\.55±1\.6150\.55\\pm 1\.6144\.72±1\.9944\.72\\pm 1\.9938\.54±3\.2838\.54\\pm 3\.2834\.56±0\.2934\.56\\pm 0\.2959\.24±2\.0559\.24\\pm 2\.0562\.81±0\.36\\boldsymbol\{62\.81\\pm 0\.36\}4\.8%49\.12±1\.7249\.12\\pm 1\.7252\.86±2\.2052\.86\\pm 2\.2049\.97±1\.6549\.97\\pm 1\.6532\.75±5\.3632\.75\\pm 5\.3634\.50±0\.2734\.50\\pm 0\.2756\.79±1\.8456\.79\\pm 1\.8463\.86±0\.46\\boldsymbol\{63\.86\\pm 0\.46\}9\.6%50\.19±2\.0350\.19\\pm 2\.0359\.42±1\.8659\.42\\pm 1\.8649\.87±2\.1649\.87\\pm 2\.1640\.56±7\.9640\.56\\pm 7\.9634\.59±0\.3334\.59\\pm 0\.3358\.58±1\.7058\.58\\pm 1\.7065\.74±0\.17\\boldsymbol\{65\.74\\pm 0\.17\}

## IVEXPERIMENTS

### IV\-AExperimental Setup

TABLE II:Overview of the datasets\.Datasets\#Nodes\#Nodestypes\#Edges\#EdgetypesTarget\#ClassesDBLP26,1284239,5666author4ACM10,9424547,8728paper3IMDB21,420486,6426movie5

#### IV\-A1Datasets

We evaluate HGC\-RC on three widely used heterogeneous graph benchmarks:ACM\[[67](https://arxiv.org/html/2607.03097#bib.bib11)\],DBLP\[[50](https://arxiv.org/html/2607.03097#bib.bib12)\], andIMDB\[[50](https://arxiv.org/html/2607.03097#bib.bib12)\]\. Following the standard HGB setting,*paper*nodes in ACM,*author*nodes in DBLP, and*movie*nodes in IMDB are treated as target node types, with node labels split into 24%, 6%, and 70% for training, validation, and testing, respectively\. We evaluate all methods under four condensation ratios, i\.e\.,1\.2%1\.2\\%,2\.4%2\.4\\%,4\.8%4\.8\\%, and9\.6%9\.6\\%\.

#### IV\-A2Baselines

We compare HGC\-RC with representative graph reduction and condensation baselines, includingRandom\-HG,K\-Center\-HG,Coarsening\-HG,GCond,GCPA, andHGCond\. Random\-HG randomly samples nodes under the same budget\. K\-Center\-HG selects representative nodes in the embedding space\. Coarsening\-HG applies topology\-based graph coarsening\. GCond and GCPA are homogeneous graph condensation methods transferred to the heterogeneous setting through a homogenized graph view for fair comparison\. HGCond is a heterogeneous\-specific condensation baseline\. All methods are evaluated under the same condensation ratios and downstream task\.

#### IV\-A3Implementation Details

We use SeHGNN preprocessing to generate semantic\-enhanced embeddings and then perform role\-aware clustering in the embedding space\. For SeHGNN, the hidden dimension and embedding size are both set to 512\. We use 2 propagation layers for feature preprocessing, while the number of task layers is set to 3, 1, and 4 on DBLP, ACM, and IMDB, respectively\. The dropout rate is 0\.5 for all datasets, and residual connections are enabled on DBLP\. We train the embedding model with Adam, using learning rate 0\.001 and weight decay 0, for 200 epochs with early\-stopping patience 50\. Unless otherwise specified, the same condensation ratio is applied across node types, and spectral clustering is used by default\. For downstream evaluation, we adopt SeHGNN as the HGNN backbone and report mean accuracy and standard deviation over 5 independent runs\. For condensed adjacency construction, we setα=10\\alpha=10,δ=0\.5\\delta=0\.5, and define the relation\-specific thresholdβr\\beta\_\{r\}as the mean of nonzero normalized inter\-cluster connectivity scores for relationrr\.

### IV\-BMain Results

Table[I](https://arxiv.org/html/2607.03097#S3.T1)reports node classification accuracy on ACM, DBLP, and IMDB under different condensation ratios\. Overall, HGC\-RC achieves competitive performance across all settings and the best results in most of them, indicating that the proposed role\-aware condensation strategy preserves substantial downstream utility under severe compression\.

OnACM, HGC\-RC performs best across all evaluated ratios and remains relatively close to the full\-graph performance, suggesting that class\-partitioned target condensation preserves discriminative information effectively\. OnDBLP, HGC\-RC is weaker than HGCond at the two lowest ratios, but becomes slightly better at higher ratios, which suggests that the proposed clustering\-based condensation benefits from a less restrictive budget\. OnIMDB, HGC\-RC achieves the best performance across all ratios, highlighting the usefulness of preserving supportive non\-target semantics in heterogeneous graphs with complex interactions\.

Overall, HGC\-RC provides a favorable accuracy\-compression trade\-off while avoiding expensive iterative synthetic graph optimization\.

![Refer to caption](https://arxiv.org/html/2607.03097v1/x2.png)Figure 3:Runtime comparison with other methods\.
### IV\-CEfficiency Analysis

Figure[3](https://arxiv.org/html/2607.03097#S4.F3)compares the condensation time of HGC\-RC with HGCond and GCond on ACM, DBLP, and IMDB\. HGC\-RC is consistently more efficient than both optimization\-based baselines across datasets and condensation ratios, especially under larger budgets\.

This advantage comes from avoiding repeated gradient matching and synthetic graph optimization\. Instead, HGC\-RC relies on a one\-shot pipeline of semantic embedding extraction, role\-aware clustering, and direct graph reconstruction\. Although the absolute runtime varies across datasets, HGC\-RC maintains a clear condensation\-time advantage in all evaluated cases\.

TABLE III:Ablation study at 2\.4% condensation ratio\.Δ\\Deltadenotes the performance change \(Variant−\-HGC\-RC\) on the same dataset\.DatasetVariantAccuracy \(%\)Δ\\DeltaIMDBHGC\-RC62\.81±0\.3662\.81\\pm 0\.36–w/o semantic embedding59\.28±0\.4559\.28\\pm 0\.45−3\.53\-3\.53w/o class partition59\.66±0\.5559\.66\\pm 0\.55−3\.15\-3\.15DBLPHGC\-RC89\.92±1\.0789\.92\\pm 1\.07–w/o semantic embedding82\.11±0\.9182\.11\\pm 0\.91−7\.81\-7\.81w/o class partition86\.03±0\.4986\.03\\pm 0\.49−3\.89\-3\.89ACMHGC\-RC91\.26±0\.6891\.26\\pm 0\.68–w/o semantic embedding89\.89±0\.1789\.89\\pm 0\.17−1\.37\-1\.37w/o class partition88\.20±2\.8288\.20\\pm 2\.82−3\.06\-3\.06
### IV\-DAblation Study

We conduct ablation studies at the2\.4%2\.4\\%condensation ratio on ACM, DBLP, and IMDB to evaluate two key components: semantic\-enhanced embedding and class\-partitioned target clustering\. Table[III](https://arxiv.org/html/2607.03097#S4.T3)reports the results, whereΔ\\Deltadenotes the performance gap between each variant and the full HGC\-RC model\.

Removing semantic\-enhanced embedding consistently degrades performance on all datasets, with the largest drop observed on DBLP\. This suggests that semantic preprocessing organizes heterogeneous nodes into a more informative representation space for subsequent clustering\.

Removing class partition also causes clear drops across all datasets, indicating that target\-node condensation should preserve label\-aware structure rather than treating all target nodes uniformly\. In particular, class\-partitioned clustering helps maintain class balance and reduces the risk of merging semantically different classes into overly coarse condensed target nodes\.

Overall, the ablation results support the two main design choices in HGC\-RC: semantic\-enhanced embedding provides a more informative clustering space, and role\-aware target condensation improves discriminative preservation under high compression\.

## VCONCLUSIONS

This paper presentsHGC\-RC, an efficient role\-aware framework for heterogeneous graph condensation\. By combining semantic\-enhanced embedding extraction, hybrid clustering for target and non\-target nodes, and cluster\-level graph reconstruction, HGC\-RC produces compact training graphs without costly iterative optimization\. Experimental results on three heterogeneous benchmarks show that HGC\-RC achieves competitive accuracy under high compression together with substantially reduced condensation cost\. Future work includes evaluating broader backbone generalization and improving robustness under noisy structures and more challenging real\-world heterogeneous settings\.

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