social network analysts

Abstract: Federated hypergraph learning with latent cross-client hyperedge correspondence poses fundamental identifiability and computational challenges, as the same local release can correspond to multiple global hypergraph structures. We characterize the tractability of recovering these latent correspondences, showing tractable pairwise assignment but generally intractable multi-client hyperedge matching. Building on this characterization, we derive a cross-entropy decomposition that reveals when local prediction can outperform predictors fitted with additional cross-client information. Motivated by this principle, we introduce Federated Adaptive Spectral Training with Representation Alignment (FedASTRA), which learns correspondence-invariant diffusion representations through adaptive heat diffusion and masked latent prediction while communicating model parameters only. We establish its asymptotic optimality with respect to the permitted local information and prove global population-risk convergence under explicit conditions on recovery, representation, and update alignment. Experiments on eight real-world datasets demonstrate the effectiveness of FedASTRA against identifier-free federated graph and hypergraph methods. On ogbn-papers100M, FedASTRA reaches the performance-communication Pareto frontier, achieving 50.07 Accuracy and 29.73 Macro-F1 while communicating only 59.60 MiB per round.

Abstract: Heterophilous graphs are prevalent in real-world applications, where connected nodes often exhibit dissimilar attributes or belong to different classes, posing significant challenges to conventional graph learning methods based on homophily. This limitation becomes particularly pronounced in generalized category discovery (GCD), which requires models to recognize known classes and discover novel ones using labels from known classes only. However, existing graph GCD methods typically rely on aforementioned homophily-based inductive biases, which are ill-suited to heterophilous graphs. Meanwhile, although current heterophilous graph learning methods exploit diverse neighborhood signals, their selection and fusion are often guided by supervision across all classes, including novel classes whose labels are unavailable in GCD. These limitations raise a key question: how can heterogeneous neighborhood information be effectively leveraged for category discovery without any novel-class supervision? To answer this question, in this study we propose HeteGCD, a new statistics-aware dual-prototype learning perspective for generalized category discovery on heterophilous graphs. The key idea is to examine both statistics of local attribute differences and neighborhood class distribution to extract discriminative information in feature and probability spaces simultaneously. Specifically, a gated dual-stream encoder integrates both node attributes and local attribute-difference statistics to learn informative node representations. Afterwards, a dual-prototype classifier combines feature-based similarity with distribution-based consistency to support category discovery. Experiments on five heterophilous graphs show that HeteGCD achieves competitive performance against 24 baseline combinations.

Abstract: Temporal hypergraphs provide an interesting representation for many social systems, as they integrate both the temporal and group nature of social interactions. Designing models of time-varying hyper-networks yields thus a convenient way to generate surrogates of empirical social systems, to understand the mechanisms underlying their emergent properties, and to investigate the evolution of dynamical processes taking place on such structures. Here, we focus on a specific and powerful class of these models, the activity-based temporal hypergraphs. We show how activity mechanisms provide control over the time scale of the dynamics, allow high modelling flexibility, and capture heterogeneity in agents' behavior. We also highlight how the activity can straightforwardly be extracted from empirical data to create surrogate datasets. We present paradigmatic examples of such models: the higher-order activity-driven models (HADx), which show that different underlying rules for the selection of active interactions produce different higher-order dynamics; the Emerging Activity Temporal Hypergraph model (EATH), able to generate surrogates of empirical systems by using higher-order mechanisms driven by both activity and group memory. We conclude discussing future perspectives for activity-based temporal hypergraphs, highlighting the potential of this framework to bridge realistic modelling of social dynamics with the study of the complex dynamical process they can support, from social contagion to opinion dynamics.

Abstract: Classifying whole hypergraphs requires a fixed-length description of inputs whose numbers of vertices and hyperedges vary. Frequent sub-hypergraph patterns provide such a description, but previous work records only whether each pattern is present, which loses two kinds of information: how large the overlap between two hyperedges is, and how much of a hypergraph each pattern makes up. We extend frequent sub-hypergraph mining with overlap labels, the binned intersection size of two pattern hyperedges inherited from the target hypergraph, and represent each hypergraph by the relative frequency of each mined pattern. The vocabulary is mined from training hypergraphs only and then frozen, and validation and test hypergraphs are matched against it. A support rule that depends on pattern size keeps the vocabulary small. On the six hypergraph-classification datasets of DHG-Bench, with a single configuration chosen on validation scores, the method has a higher mean Macro-F1 than the best published mean on five datasets, by 18.67 points on Twitter-Friend and 10.02 points on Steam-Player; on RHG-3 it is 0.21 points lower. Ablations show that on Steam-Player and Twitter-Friend, replacing relative frequencies with presence lowers Macro-F1 by about 18 points, and that removing overlap labels lowers it by 4 to 9 points.

Abstract: Boolean matrix multiplication is a fundamental operation in many graph-based applications, including web and social network analysis, information retrieval, and graph query evaluation. However, conventional sparse representations such as CSR}/CSC still incur significant space and time costs on large graphs. In this work, we introduce a method for multiplying Boolean matrices based on a biclique-based compressed representation that decomposes them into dense bipartite subgraphs, thereby capturing large sets of implicit edges. We first improve the iterative biclique extraction algorithm of Hernández and Navarro by introducing percentile-based parameter adaptation that dynamically adjusts its parameters according to the degree distribution, enhancing both extraction efficiency and compression ratio. We then extend the Schoor multiplication algorithm to operate directly on biclique-encoded matrices, thereby enabling a compositional form of multiplication where the output can also be represented as a collection of bicliques. Our experimental results on large real-world web and social graphs show that our approach achieves substantial reductions in space and computation time with respect to CSR/CSC-based representations. For example, using biclique extraction just as a tool to speed up multiplication (but retaining the CSR/CSC format) yields up to 34-fold speedups. Further, using the biclique-based representation for input and output yields up to a 10-fold reduction in space and up to a 290-fold speedup for matrix multiplication. These results demonstrate that our representation based on bicliques is both space- and time-effective to support an algebra of Boolean matrices.

Abstract: Graphs play a crucial role in many applications, ranging from drug discovery to social network modeling and astronomy. Generative models for graphs have substantially advanced in recent years, but we identify relatively simple scenarios where state-of-the-art models struggle to converge within a standard compute budget, or exhibit prohibitively slow generation times. We propose a generative architecture that achieves quality competitive with state-of-the-art models and is orders of magnitude faster at generation. Our approach is inspired by the Aldous-Hoover theorem, a classic representation theorem that characterizes any probability distribution of graphs that is invariant to permutations of node indices or exchangeable. This theorem establishes that three ingredients suffice: a graph-level latent variable, a set of exchangeable node-specific latent variables, and a so-called graphon function that maps graph- and node-level variables to the probability of an edge between any node pair. Given a training set of graphs, our exchangeable Variational Graph AutoEncoder (xVGAE) learns an approximation to their underlying graphons, as well as graph- and node-level latent variables. We show that our xVGAE encodes latent representations that correlate with graph- and node-level properties, and can (quickly, in one shot) generate new graphs that closely match key training set statistics.

Abstract: Dynamic local community detection tracks the evolving community of designated seed nodes across graph snapshots. However, it faces two critical challenges: temporal supervision uncertainty, where sparse and outdated labels fail to provide seed-specific guidance under topology changes, and unbounded error cascades, where sequential policy transfer accumulates exploration errors over long horizons. To address these challenges, we propose DISRL, a Dual-scale Incremental Semi-supervised Reinforcement Learning framework. DISRL introduces a supervision construction module that dynamically generates seed-specific guidance from sparse known communities, and a dual-scale community exploration module that stabilizes policy evolution by decoupling short-term adaptation within temporal windows from long-term parameter consolidation across windows. Furthermore, we construct a dynamic graph benchmark with diverse community evolution scenarios. Extensive experiments demonstrate that DISRL consistently outperforms state-of-the-art baselines under various dynamic settings.

Abstract: Exact forward triangle listers orient each edge of a graph by a vertex order. The order does not change the output, but it changes the work. For the adaptive lister, which scans the smaller of the two forward neighborhoods, the number of candidate tests is a known sum of minima of forward degrees, but how to optimize it had not been characterized. We show that this work is a concave function of the forward degrees, so choosing an order is concave minimization over the orientation polytope, whose vertices are the forward-degree vectors of orders. A single sort therefore rounds any point of the polytope, including the out-degree vector of any orientation, to an order with no more work, with a computable lower bound on the improvement. Minimizing the work is nevertheless NP-hard and APX-hard on triangle-free graphs of maximum degree three, and under the Unique Games Conjecture it has no polynomial-time constant-factor approximation. We also analyze logistic score relaxations and the large-graph limit of degree-based orders; on random cubic graphs, the expected work of every degree-based order is asymptotically at least $2.43$ times the expected optimum. Tangent refinement followed by iterated local search reduces the work by \HeldTIKMean\% on average on nine held-out networks fixed by a pre-registered protocol, and by \NSFrozenTILSMean\% in a supplementary rescoring, specified in advance, against a stronger reference that adds the published Neigh local search. The gains are in candidate tests; we observe no reproducible wall-clock speedup.

Abstract: We present a simple deterministic semi-streaming algorithm that computes a $(1-\varepsilon)$-approximate maximum matching in general graphs in $O(1/\varepsilon^{2})$ passes. This matches the pass complexity of the auction algorithm of Assadi, Liu, and Tarjan~[SOSA'21] for bipartite graphs, and answers Open Question~2 of Assadi~[SOSA'24 \& TheoretiCS'25]. Our approach, which we call the \emph{budgeted price approach}, is very different from the previous $\mathrm{poly}(1/\varepsilon)$-pass semi-streaming algorithms for $(1-\varepsilon)$-approximation of matching in general graphs and improves their pass complexity. All previous approaches are augmenting-path-based and use $O(1/\varepsilon^{19})$ passes by Fischer, Mitrović, and Uitto~[STOC'22], $O(1/\varepsilon^{6})$ passes by Mitrović, Mukherjee, Sankowski, and Sheu~[ICALP'25], and $O(1/\varepsilon^{4})$ passes by Izumi, Kitamura, and Yamaguchi~['25].

Abstract: Dynamic graph learning models how entities and their relations evolve from historical observations to predict future graph states. Existing methods do not fully address dynamic graph world modelling, which requires learning transitions from temporal context to future latent graph states. This is difficult for three reasons: nodes and relations rely on different historical evidence, structural evolution is path-dependent, and future snapshots provide sparse and realization-specific targets. We propose Dynamic Graph World Modelling (DyG-WM), the first framework to jointly predict future node and relation representations from temporal context by answering three questions: what has evolved, how it evolved, and what will evolve next. To capture what has evolved, a historical node-relation context encoder summarizes node-neighborhood trajectories and pair-specific histories. To characterize how it evolved, a node-relation path-signature encoder captures ordered structural changes. To predict what will evolve next, a dual-level joint-embedding objective predicts target-snapshot node and relation representations without reconstructing the raw graph. Experiments on 12 link-prediction and two node-classification datasets demonstrate the effectiveness of DyG-WM across both tasks.

Abstract: In this work, we revisit the classic Les Misérables benchmark network from the perspective of social communication. Using the 1998 film adaptation of the novel, we construct the publicly available Les Misérables Dialogue temporal text network, which explicitly distinguishes speakers, addressees, and other recipients of each utterance, along with its content and timing. Using the ten social dimensions model, we also derive multilayer network representations of the network, in which layers correspond to distinct relational dimensions. Beyond the network dataset, this work offers a general methodology for building similarly rich communication datasets from similar narrative sources.

Abstract: Frustrated Ising models of social networks mix ferromagnetic (agreement-seeking) and antiferromagnetic (antagonistic) couplings, and the antagonistic bonds are almost always placed independently at a fixed rate, yielding a +/-J spin glass. Real signed networks (Epinions, Slashdot, Wikipedia) instead show an excess of balanced triads, and perfectly balanced placement is gauge-equivalent to an unfrustrated ferromagnet. We compare three sign-placement conditions on a frustrated random-field Ising model of a polarised population, sharing an identical graph, field assignment, and edge-weight magnitudes: an independent baseline; a balance-structured condition whose camp membership coincides with each voter's field sign; and the same condition with camp labels randomly permuted, so triadic balance is identical by construction while the camp-field correlation is removed. On a confound-controlled Kolmogorov-Smirnov test of the sampled energy-gap distribution (simulated annealing), the aligned condition differs from the baseline at every density tested (p = 7.3e-8), while the permuted condition shows no significant difference (paired mean difference 0.003, 95% CI [-0.041, 0.046]). Field-camp alignment, not triadic balance alone, drives the effect. The qualitative direction follows from a known mapping; the contribution is a quantitative, confound-controlled measurement of the effect's size away from that limit, robust to parallel-tempering sampling, system sizes up to N = 300, and structural noise calibrated to real networks, while triadic balance alone produces no detectable effect at N = 90 and at most a small one at N = 180-300 (paired change in KS distance about 0.04, 95% CI upper bound below 0.09).

Abstract: Graph clustering is a fundamental task in data analysis, aiming at grouping nodes with similar characteristics in the graph into clusters. This problem has been widely explored using graph neural networks (GNNs) due to their ability to leverage node attributes and graph topology for effective cluster assignments. However, representations learned through GNNs typically struggle to capture global relationships between nodes via local message-passing mechanisms. Moreover, the redundancy and noise inherently present in graph data may easily result in node representations lacking compactness and robustness. To address these issues, we propose a conjoint framework CoCo, which captures compactness and consistency in the learned node representations for deep graph clustering. Technically, our CoCo leverages graph convolutional filters to learn robust node representations from both local and global views, and then encodes them into low-rank compact embeddings, thus effectively removing the redundancy and noise as well as uncovering the intrinsic underlying structure. To further enrich the node semantics, we develop a consistency learning strategy based on compact embeddings to facilitate knowledge transfer from the two perspectives. Our experimental results indicate that our CoCo outperforms state-of-the-art counterparts on various datasets.

Abstract: Sparse GNN training reduces computation, but deciding which edges to keep can be costly. Reusing one sparse graph is cheap, but locks training to a fixed topology, while varying it across epochs can require repeated sampling or recomputation. We introduce EDiS (Edge-Disjoint Subgraph sparsification framework), which separates one-time structural extraction from per-epoch graph composition. EDiS decomposes the graph once into cacheable edge-disjoint subgraphs, then recombines them into graphs with edge-budget constraints across epochs and retention ratios without re-extracting structure. Our default construction uses feature-based scores and successive maximum score covering forests, while the same composition mechanism also supports alternative edge selection rules. We provide a combinatorial analysis of the per-epoch sampler, the composition step that draws a training graph from the cached decomposition. We show that, under the default covering-forest selector, the stored decomposition deterministically preserves high-score cut edges, and we derive a selector-agnostic conditional bound on high-score cut survival in composed training graphs. Across 19 homophilic, heterophilic, and large-scale node classification benchmarks against 17 baselines under the same edge budget, EDiS achieves the highest mean benchmark score (accuracy/ROC-AUC) and the lowest average rank and gap-to-best among ranked methods. Ablations show the clearest benefits of structural decomposition and epoch variation at tight edge budgets.

Abstract: Attributed graph clustering aims to discover node groups by jointly exploiting node attributes and graph topology, yet its unsupervised nature makes model selection and adaptation inherently difficult. Existing methods typically train and tune a separate model for each input graph, leading to costly and fragile pipelines that often fail to transfer across graphs with different feature spaces, structural patterns, and attribute-structure correlations. In this paper, we study a one-for-all alternative: can a single model be trained once and directly applied to diverse attributed graphs without graph-specific training, fine-tuning, or hyperparameter search? We propose OFAG, a foundation model for attributed graph clustering. Building upon Prior-data Fitted Networks, OFAG learns a reusable clustering inference strategy from synthetic attributed graphs generated under broad priors over latent clusters, node attributes, and graph structures. To handle incompatible feature spaces across graphs, OFAG adopts a dimension-agnostic signal-wise graph encoder that treats each feature channel as a graph signal and models its response to shared graph filters. The model is trained with a hyperspherical clustering objective, producing clustering-friendly node representations in a single forward pass at inference time. On ten datasets, one frozen OFAG model achieves the best mean performance and average rank across NMI, ACC, ARI, and F1, while completing all ten datasets in 12.43 minutes total---over 6* faster than the second-fastest baseline and nearly 28* faster than the second-best on clustering quality. Our code and pretrained checkpoint are available at https://github.com/Cloudy1225/OFAG, allowing practitioners to directly apply OFAG to their own attributed graph datasets without additional training or tuning.

Abstract: Hypergraphs offer a natural framework for modeling networked data, where dependencies among entities are governed by higher-order interactions. While hypergraph learning methods such as hypergraph neural networks have demonstrated remarkable predictive performance, most existing approaches rely on black-box message-passing architectures, making it difficult to disentangle the contributions of node attributes and higher-order structural information. To address this challenge, we introduce the hypergraph neural additive network (HGNAN), an inherently interpretable framework for learning on hypergraph-structured data. HGNAN extends classical neural additive models to higher-order relational data by integrating feature-wise nonlinear decomposition with hypergraph-aware structural aggregation, enabling transparent prediction for both node- and hyperedge-level tasks. Extensive experiments on benchmark datasets demonstrate that HGNAN achieves performance comparable with state-of-the-art hypergraph learning methods while providing intrinsic and meaningful interpretability.

Abstract: Hypergraphs record multi-way interactions among entities. Extracting information from the combinatorial structure underlying observed multi-way interactions is a central task in many real-world problems. Existing methods face several limitations. First, many deep architectures for hypergraphs do not explicitly exploit the potential low-rank structure, which can sacrifice parsimony and interpretability in the learned representations. Second, many low-rank-based methods operate on tensor representations, which typically require hyperlinks to have uniform sizes and thus limit their applicability to general hypergraphs with non-uniform hyperlink sizes. Third, many methods ignore the fact that hyperlinks often arise from heterogeneous mechanisms. For example, medical symptoms may co-occur in the profiles of patients with very different conditions, and such heterogeneity should be incorporated into the learning process. In this work, we develop a general framework for hypergraph representation learning using hyperlink random effects while exploiting the low-rank structure in hypergraphs. The proposed framework accommodates latent heterogeneity in hyperlink formation while preserving entity interaction patterns. We establish identifiability of the model parameters and theoretical guarantees of representation-level recovery under this framework. The framework allows flexible specifications for the hyperlink random effects; in this paper, we study three choices: categorical, Gaussian mixture, and score-based effects, and develop corresponding estimation algorithms. Through simulation studies, we demonstrate the effectiveness of the proposed method in recovering latent structure and capturing heterogeneous interaction patterns. Empirical studies on real-world hypergraph datasets further illustrate the practical utility of our approach.

Abstract: Multilayer networks allow the modeling of interactions between the same entities across different contexts, such as temporal observations, varying settings, or interactions of different types. The goal of community detection in multilayer networks is to identify groups of nodes exhibiting similar connectivity patterns, which may vary across layers. We propose a method based on a joint nonnegative symmetric matrix trifactorization for community detection in multilayer networks, where each graph is approximated by a nonnegative symmetric matrix trifactorization. Our approach enforces constraints on the factor matrices so that communities are disjoint and shared across layers, while allowing each layer to have its own connectivity patterns and node degrees. This flexibility enables the model to capture both local and global structural variations across layers. We also develop an algorithm to efficiently solve this problem. We evaluate multilayer community detection methods using the multilayer degree-corrected stochastic block model (MDCBM), a flexible framework for generating realistic multilayer graphs with heterogeneous degrees and varying connectivity patterns. Experiments show that our method reliably detects communities across diverse regimes, whereas existing state-of-the-art approaches are often limited by restrictive structural assumptions.

Abstract: Learning analytics increasingly represents the relations in co-occurrence data---codes in a window of discourse, participants in a thread, tags on a post---as simplicial complexes and analyses them with persistent homology. The standard approach uses the clique complex. Because its simplices are determined by the pairwise network alone, it cannot distinguish "three elements co-occurred together" from "each of the three pairs co-occurred separately". The Dowker complex, in contrast, takes as simplices the sets of entities actually observed to co-occur. We compare analyses based on these two complexes. First, we show that, on the same 1-skeleton, the Dowker complex is a subcomplex of the clique complex, the map on first homology induced by the inclusion is surjective, and its kernel is generated by phantom triangles that never co-occurred; that is, the clique construction can only erase holes. We then test this on real data. On four Stack Exchange data sets, 46--91% of clique triangles are phantom and 522--1,970 holes are erased. On the example data of the learning analytics R packages tna/Nestimate, the first Betti number $β_1$ of the clique complex is 0 at every threshold, whereas the Dowker complex detects holes. Against a degree-preserving null model, the Dowker complex departs strongly in five of the six data sets. Moreover, this difference does not appear in the fixed-threshold analyses used in practice. We conclude that the construction should follow the data type and that, for observed groups, the Dowker complex is the appropriate choice; it fills a gap in current tooling. Code is available at https://github.com/igu-lab/beyond-the-clique.

Abstract: While foundation models have revolutionized natural language processing and computer vision by leveraging universal vocabularies, Graph Machine Learning (GML) remains fractured due to the absence of a unified feature and structural representation across diverse domains. Existing works claiming to be Graph Foundation Models (GFMs) are typically restricted to node-level predictions or require fixed feature dimensions, failing to provide a truly task-agnostic backbone for the full spectrum of graph learning applications. In this paper, we introduce the Universal Classifier (UC), which supports arbitrary feature and class cardinalities, unifying node-, edge-, and graph-level objectives under a single similarity-based classification objective. The UC reformulates all node-, edge-, and graph-level prediction tasks as maximizing similarity in the latent space: by lifting heterogeneous features and labels into 3D latent tensors, the model learns transferable features independent of specific input schemas. This architecture allows a single pre-trained model to generalize to node classification, node regression, and link prediction across unseen graphs with varying feature semantics. Experiments show strong zero-shot transfer performance across node-, link-, and graph-level tasks.

Abstract: Existing interpretable graph additive models still face limitations in either computational scalability or modeling flexibility. In terms of structural modeling, previous approaches either face quadratic scaling costs or sacrifice explicit source-to-target contribution decomposition. In terms of feature components, they rely either on per-feature neural networks or on single shared bases with limited feature specialization. We address both problems by introducing HARMONIA: Interpretable Graph Learning through Mixtures of Neural Bases, an interpretable-by-design framework. For feature modeling, HARMONIA introduces a Mixture of Neural Bases (MoNB), which routes features to specialized basis experts, enabling parameter sharing without sacrificing feature-specific specialization. For structural modeling, HARMONIA uses Relative Random Walk Probabilities (RRWP) to capture multi-hop and multi-path relationships, and proposes Sparse RRWP Aggregation (SRA) to compute these interactions through sparse graph propagation without quadratic pairwise complexity. HARMONIA retains a simple additive form in which predictions decompose into feature responses modulated by structural influence. Empirically, HARMONIA achieves stronger explanation recovery than existing interpretable graph baselines while maintaining competitive predictive performance and scaling to graphs with millions of nodes. These results show that interpretable graph learning can remain both faithful and scalable without sacrificing predictive effectiveness.

Abstract: Learning transferable representations for dynamic text-attributed graphs (DyTAGs) requires models to capture underlying interaction dynamics that persist across domains. However, existing methods tend to overfit to domain-specific structural, temporal, and semantic patterns, limiting edge classification performance under distribution shifts. To expose and address this, we formally establish a leave-one-domain-out (LODO) transfer learning protocol for edge classification on DyTAGs. Under this protocol, we demonstrate that state-of-the-art self-supervised methods for dynamic graph learning perform poorly when transferred to unseen domains. Strikingly, existing methods underperform a structurally and temporally unaware Bag of Events (BoE) model we introduce, which inputs only unordered sequences of node and edge text features. Proceeding from the BoE, we propose Spatio-Temporal Semantic Alignment (STSA), which integrates a spatio-temporal encoder that fuses representations of time deltas and node occurrence frequencies into a unified manifold. STSA is trained with a Contrastive Semantic Forecasting objective, which anchors edge representations to a multi-domain textual latent space initialized by a pretrained language model, providing a robust prior that outperforms BoE and all existing methods we evaluate.

Abstract: Graph neural networks (GNNs) rely on message passing over graph edges, making their computational and memory costs strongly dependent on graph density. Graph sparsification offers a natural way to reduce these costs, but removing edges indiscriminately can distort important communication structure and degrade predictive performance. We introduce Scaffold, a topology-based, unsupervised graph sparsification framework derived from support graph theory preconditioners. Scaffold explicitly controls two complementary structural quantities: dilation, which measures the length of rerouting paths induced by removed edges, and congestion, which measures how strongly these rerouted paths concentrate on the retained support. By jointly controlling dilation and congestion, Scaffold preserves short communication paths while avoiding structural bottlenecks. To our knowledge, Scaffold is the first scalable GNN sparsification framework to use a joint supporting-path dilation-congestion criterion. Across 19 homophilic and heterophilic benchmarks spanning small to large graphs, Scaffold achieves the best aggregate rank among the evaluated sparsification and related methods. Using only 10%-50% of the original edges per sparse support, Scaffold recovers or closely approaches full-graph GNN performance while using less than half the memory of full-graph training and reducing end-to-end training time, including sparsification overhead. We provide an open-source software package at https://github.com/siddhartha047/Scaffold.

Abstract: Multimodal attributed graphs connect entities, visual content, language, and observed relations. Learning one foundation across such graphs requires more than compressing each node into a fused Euclidean vector. The representation must preserve entity semantics, construct interaction state from graph neighborhoods, and expose that state to prediction units with different geometry. Our empirical study shows why these requirements are inseparable. Higher-grade channels recover pair relations across the foundation graphs, specialized queries reveal information hidden by a generic readout, and rigid blade isolation removes cross-grade capacity. We therefore introduce ICE (Interaction-aware Clifford Encoder), a multimodal graph foundation model built on a node-indexed Clifford latent field. Topology, text, and images enter explicit Cl(3) addresses. Edge-aware geometric products transform these directions into scalar, bivector, and trivector relations over observed neighborhoods. A protected Grade-1 route preserves entity semantics, while the full grade and depth bank remains available to fresh node and link heads. We establish exact cross-grade reachability, node-permutation equivariance, and a bound on the task residual around the semantic score. Experiments span one shared foundation over eleven graphs, six node-classification datasets, three link-prediction datasets, and matched few-shot tasks. ICE ranks first in all 30 reported supervised and few-shot comparisons. Core removals reduce every task summary, and mechanism controls connect the gains to higher-order transport, retained multidepth structure, semantic protection, and direct field access.

Abstract: Detection of overlapping communities is essential for modelling networks in which nodes participate simultaneously in multiple structural or functional groups. Existing graph neural network approaches commonly rely on local message passing, which can obscure community boundaries through smoothing and limit the representation of structurally relevant long-range dependencies. We introduce Diffusion-Induced Spatial Attention Community Detection (DISCO), a deep-learning framework that combines a structural prior derived from influence spreading dynamics, sparse multi-head attention, and non-negative community-affiliation learning. The prior identifies candidate interactions beyond immediate graph neighbours and biases attention according to their structural proximity, while a Bernoulli-Poisson edge-reconstruction objective enables overlapping community inference from node attributes and structural profiles, or both. Benchmark experiments show that DISCO performs competitively against established graph convolutional and graph attention approaches across different input configurations. To demonstrate its practical applicability, we present a proof-of-concept cybersecurity use case in which changes between community assignments inferred from consecutive communication-network snapshots provide an interpretable anomaly signal. Temporal community similarity identifies structural deviations, while node-level contributions help locate the devices associated with them. DISCO therefore provides both a flexible method for overlapping community detection and a foundation for analysing structural change in dynamic networks.

Abstract: Graph neural networks have achieved strong performance in node classification by aggregating information from graph neighborhoods. However, a single aggregation mechanism may be insufficient to capture diverse structural patterns across graph datasets. Moreover, independently training multiple structural branches can introduce substantial overhead without necessarily producing stable node representations. To address these issues, this paper proposes PreGS, a parameter-transfer-based multi-expert graph neural network framework. PreGS first pretrains a multi-head graph attention network (GAT) and transfers the linear transformation weights of its first-layer attention heads to multiple GraphSAGE experts. The transferred experts are frozen and used as complementary structural branches. The fused raw node features, GAT head representations, and GraphSAGE expert representations are fed into a multilayer perceptron (MLP), whose output is further fused with the pretrained GAT logits. Based on PreGS, we further develop PreGSv2, which introduces source-level weighting and a structural gating mechanism for adaptive multi-source feature integration. Experiments on eight public graph datasets show that PreGS and PreGSv2 achieve competitive performance against representative graph neural network baselines. Ablation, parameter-transfer, sensitivity, aggregator, visualization, and training-time analyses further validate the effectiveness and stability of the proposed framework. The code and datasets are available at https://github.com/LH-Czc/PreGS.

Abstract: Graph-based ranking methods such as PageRank can amplify structural disparities in networks, motivating fairness-aware ranking mechanisms for sensitive groups. Locally Fair PageRank (LFPR) enforces fairness through local propagation, but exact computation requires repeated iterations until convergence, limiting scalability on large graphs. We develop a scalable analytical framework for approximating Neighborhood Locally Fair PageRank and Uniform Locally Fair PageRank. By introducing a group-aware heterogeneous mean-field representation, the framework aggregates structurally similar nodes into degree classes and derives closed-form approximations of stationary LFPR scores, avoiding repeated propagation over the fairness-aware transition matrix. We develop a One-Step Refinement (ORF) mechanism that applies the fairness-aware propagation operator once to the mean-field estimate, incorporating node-specific neighborhood information without iterative convergence. The fluctuation analysis characterizes degree-dependent variability around the mean-field solution and shows that the coefficient of variation decreases with increasing in-degree. The mean-field approximation reduces the computational cost of exact LFPR from iterative graph-scale propagation to linear-time node-level estimation, while ORF requires one graph traversal. Experiments on six real-world networks show strong agreement with exact LFPR scores and rankings, preservation of group-level fairness, and substantial runtime reductions. The mean-field approximation reduces complexity to $\mathcal{O}(n)$, while ORF improves accuracy with $\mathcal{O}(m+n)$.

Abstract: The balanced butterfly is a fundamental primitive for analyzing signed bipartite graphs and provides a basis for studying higher-order structural properties, such as clustering coefficients and community structure. Despite its importance, existing approaches primarily rely on serial algorithms for balanced butterfly counting, which become inefficient on large-scale graphs. To address this limitation, we propose a distributed algorithm, D-BBC, based on a hybrid MPI+TBB framework that exploits MPI for inter-process communication and Intel TBB for intra-node parallelism. We conduct an experimental assessment of the proposed approach across 15 real-world datasets. Experimental results demonstrate that, on a single-node distributed system, D-BBC achieves average speedups of 1321x and 16.2x over the serial BB2K and multi-core M-BBC implementations, respectively. Furthermore, D-BBC achieves a maximum speedup of 23.58x over the distributed baseline S-Monarch in terms of end-to-end execution time. These results demonstrate the efficiency of the proposed distributed approach and its potential to enable high- performance signed motif analysis on large-scale bipartite graphs.

Abstract: We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.

Abstract: Degree-sequence realizability is the combinatorial basis of configuration models, but degree constraints alone do not ensure the preservation of graph dynamics. Hence, configuration models are unable to recover centrality measures, unless these are strongly correlated with the degree sequence. To address this matter, we introduce EP-realizability, the analogue problem induced by an equitable partition (EP): given the EP of a graph, decide whether the partition is realized by a simple undirected loopless graph and therefore construct such a graph. After defining the problem, we solve it by reducing it to sub-problems related to Havel--Hakimi and the Gale--Ryser theorem. We also face the challenge of solving the problem with an Approximate Equitable Partition ($\varepsilon$-EP), so that it is possible to reconstruct a network starting from partial and more privacy-preserving information. We evaluate privacy with edge overlap, deriving also, for our proposed $\varepsilon$-EP-realizability solution, a predictor for this metric. Experiments on Karate, Cora, CiteSeer and PubMed datasets show that our algorithm achieves a favourable and tunable privacy--utility trade-off, comparing the results with Havel--Hakimi algorithm, Newman's configuration model and a stochastic block model. Finally, both with real data and random graphs, we show that our algorithm has approximately linear time complexity with respect to the number of edges.

Abstract: Recently, researchers have proposed a graph pooling operation, akin to the pooling process in conventional convolutional neural networks (CNN), aimed at reducing the computation cost of Graph convolutional neural networks (GCNNs). While most GCNN-based methods treat graph pooling as a node clustering problem and propose learning a cluster assignment matrix, existing clustering-based pooling methods tend to focus solely on the rough topology information of graphs, neglecting the exploitation of higher-order mutual connections among neighbors. In terms of message passing on graph, the ease of information passing on edges reflects the closeness between neighboring nodes, which significantly relies on the interconnectivity among neighbors. In this study, we address this gap by considering such local connection information and introducing a novel graph pooling method named RicciPool. We introduce discrete graph curvature, particularly Ollivier-Ricci curvature, as a measure of higher-order connectivity around an edge. Subsequently, we construct an Ollivier-Ricci flow formula to reweigh edge weights, leveraging the crucial information provided by Ricci curvature, particularly vital for extracting clusters in graphs. Building upon this foundation, we utilize the spectral clustering technique to learn a new cluster assignment matrix. Experimental results on multiple bioinformatics protein datasets and social networks underscore the effectiveness of our proposed method.

Abstract: Graph property testing asks whether a massive graph satisfies a given property, or is far from doing so, using only a sublinear number of queries to the graph. Since property testers typically inspect only a small, randomly sampled portion of the input, they appear naturally compatible with differential privacy and privacy amplification by subsampling. Despite this, few results link these two fields. We initiate a systematic study of differentially private graph property testing with the goal of designing efficient testers with formal privacy guarantees in the dense and bounded-degree graph models. We develop new privacy amplification theorems for several widely used graph-sampling procedures such as induced subgraph sampling, random walks and k-disc sampling. We then leverage these privacy amplification techniques to design a private canonical tester in the dense graph model, as well as private bipartiteness testers and subgraph freeness testers in the dense and bounded-degree graph models. Finally, using the new privacy amplification theorem for k-disc sampling, we prove that every property of hyperfinite graphs is privately testable. The resulting query complexities of our private testers are comparable to those of their non-private counterparts.

Abstract: We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.

Abstract: Temporal graph learning models the evolution of dynamic systems, where both structural interactions and semantic states change over time. However, existing benchmarks primarily emphasize structural evolution via temporal link prediction (TLP), while support for semantic evolution remains limited. Although temporal node classification (TNC) is sometimes included, it is typically restricted to simplistic binary settings that fail to capture realistic semantic drift. Moreover, commonly used datasets exhibit high link repetition, leading to inflated performance estimates and obscuring true model capability. To address these limitations, we introduce \textbf{TTGBench}, a new benchmark that jointly evaluates structural and semantic evolution. TTGBench comprises six real-world, text-rich datasets characterized by \emph{Dual Volatility}, enabling rigorous and fair evaluation of existing models. Notably, it is the first benchmark to support both multi-class and multi-label TNC, filling a critical gap in evaluating temporal semantic drift. We conduct a comprehensive evaluation of 17 state-of-the-art methods across Temporal Graph Neural Networks (TGNNs) and Large Language Model (LLM)-based paradigms. The results reveal a clear \emph{capability divide} between the two paradigms: TGNN-based methods excel at structural prediction but fail at semantic tracking, whereas LLM-based predictors show the opposite trend. Through in-depth analysis, we uncover their fundamental limitations and provide insights for developing more comprehensive temporal graph models.