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arXiv2026

Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction

Graph link prediction (LP) plays a critical role in socially impactful applications such as job recommendation and friendship formation, making fairness a critical concern in this task. While many fairness-aware methods manipulate graph structures to mitigate prediction disparities, the topological biases inherent to social graphs remain poorly understood and are consistently conflated with homophily alone. In this work, we study the relationship between structural biases and fairness outcomes in LP. To this end, we formalize a taxonomy of topological bias measures and introduce a graph generation method producing a diverse corpus of synthetic graphs with controlled structural properties. Using this corpus, we show empirically that fairness outcomes are strongly correlated with graph topology, and that current fairness-aware methods remain sensitive to structural biases beyond homophily. These findings highlight the need for structurally grounded evaluations in fair graph learning.

cs.LG↗
arXiv2026

Constructing the Field of Philanthropic and Nonprofit Studies: Evidence from Citation Networks

Philanthropic and nonprofit studies (PNPS) has grown rapidly as an interdisciplinary field, yet its intellectual structure and boundaries remain only partially visible. This study maps the field by combining journal- and keyword-based retrieval with citation network analysis, natural language processing, and large language model-assisted cluster labeling. Using 60,917 Web of Science articles, we identify major topical communities, examine their structural connections, and assess how well mainstream PNPS journals represent the broader landscape of related scholarship. The results show that PNPS is a loosely connected field dominated by three distinct "power centers": nonprofit organizations, social movements, and voluntary action. The analysis also reveals a broader disciplinary footprint than commonly recognized, extending beyond the social sciences and humanities into areas such as biomedicine and technology. These findings clarify the organization of PNPS and highlight opportunities for stronger integration across research domains.

cs.SI↗
arXiv2026

Structural Change and Random Graph Models in Global Oil Trade Networks

We studied structural change in global oil trade using a network approach. Using UN Comtrade data, we examined the temporal evolution of international trade networks, with an emphasis on crude oil. Weighted in-degree identified major changes in country rankings in 1991, 2011, 2017, and 2021, while PageRank detected pronounced changes around 1991 and 2024. The Louvain algorithm identified clear geographic communities within the overall trade network. In the oil trade network, modularity declined from the 1990s to the 2010s, with node2vec embeddings showing weaker clustering in 2011 than in 1991. We also compared the oil trade network with several random graph models using 3- and 4-node subgraph profiles and machine learning classification. The oil trade network was consistently classified as a Chung-Lu graph, while the Geometric model was not favored, suggesting that a model based on the degree distribution better matched its subgraph profiles than the other models considered.

cs.SI↗
arXiv2026

Walk based Laplacians for Modeling Diffusion on Complex Networks

We develop a novel framework for modeling diffusion on complex networks by constructing Laplacian-like operators based on walks around a graph. Our approach introduces a parametric family of walk-based Laplacians that naturally incorporate memory effects by excluding or downweighting backtracking trajectories, where walkers immediately revisit nodes. The framework includes: (i) walk-based Laplacians that count all traversals in the network; (ii) nonbacktracking variants that eliminate immediate reversals; and (iii) backtrack-downweighted variants that provide a continuous interpolation between these two regimes. We establish that these operators extend the definition of the standard Laplacian and also preserve some of its properties. We present efficient algorithms using Krylov subspace methods for computing them, ensuring applicability of our proposed framework to large networks. Extensive numerical experiments on real-world networks validate the modeling flexibility of our approach and demonstrate the computational efficiency of the proposed algorithms, including GPU acceleration.

cs.SI↗
arXiv2026

SnapScope: A Platform for City-Scale Collection and Exploration of Public Snap Map Data

Snapchat's Snap Map is an ephemeral stream of geotagged public video and image stories, but the platform provides no documented API, no prior work describes a reproducible system for collecting this data at city scale, and no tool exists for managing and exploring the collected data interactively. We present SnapScope, an integrated platform that pairs a back-end collection pipeline with a web-based front end for scraper management, interactive data exploration, side-by-side neighborhood comparison, and data export. We deploy the platform over Riyadh, Saudi Arabia, collecting 515,364 unique public snaps across 23 days on a 1 km grid of 2,740 query points. A saturation probe over 21 consecutive runs shows that 94.8% of returned observations are duplicates of already-stored records. We provide a privacy-safe aggregate dataset under CC BY 4.0. The platform is city-agnostic and redeployable by substituting grid coordinates and boundary polygons.

cs.SI↗
arXiv2026

Hyperedge Anomaly Detection with Hypergraph Neural Network

Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of entities, which is essential in many real-life applications. Hypergraph learning algorithms have been well-studied for numerous problem settings, such as node classification, link prediction, etc. However, much less research has been conducted on anomaly detection from hypergraphs. Anomaly detection identifies events that deviate from the usual pattern and can be applied to hypergraphs to detect unusual higher-order associations. In this work, we propose an end-to-end hypergraph neural network-based model for identifying anomalous associations in a hypergraph. Our proposed algorithm operates in an unsupervised manner without requiring any labeled data. Extensive experimentation on several real-life datasets demonstrates the effectiveness of our model in detecting anomalous hyperedges.

cs.LG↗
arXiv2026

A Network Science Perspective on Evaluating Deep Graph Generative Models

Traditional network models from network science, such as the Erdos-Renyi and configuration models, generate random networks that reproduce few selected topological properties observed in real-world networks. Deep graph generative models emerge as a data-driven approach, leveraging deep neural network architectures to learn complex structural distributions directly from real-world networks to generate more realistic synthetic networks. Because real social contact networks cannot be shared due to privacy risks, synthetic networks serve as an alternative for developing and evaluating epidemic mitigation strategies. In this work, we evaluate deep graph generative models as well as the configuration from a network science perspective by assessing both the topological similarity between generated and real-world networks and their utility in identifying effective node immunization strategies to sup- press epidemic/misinformation spreading. It is found that two deep graph generative models produce synthetic networks that closely resemble the structural properties of real-world networks, enabling them to identify effective immunization strategies.

cs.SI↗
arXiv2026

Behavioral calibration of mobile-phone GPS data for population-representative analyses

Mobile phone mobility data have transformed the study of human behavior, but demographic and behavioral biases can compromise their representativeness and distort population-level inference. Existing calibration approaches primarily address demographic and geographic representativeness, leaving behavioral discrepancies largely uncorrected. Here we introduce the Behavioral Population (BePop) framework, which jointly calibrates mobility data to representative demographic and behavioral distributions using census data and time-use surveys. BePop embeds mobility sequences into behavioral profiles and estimates person-level weights that align both population composition and daily activity patterns. Across three U.S. metropolitan areas, the framework consistently improves agreement between GPS-derived mobility and representative behavioral distributions, including time allocation, activity transitions, and mobility motifs. Calibration also substantially alters downstream mobility indicators, demonstrating that behavioral biases can propagate into commonly used mobility measures. Our results establish behavioral representativeness as a critical complement to demographic calibration and provide a general framework for population-representative mobility inference.

physics.soc-ph↗
arXiv2026

On graphs with modularity zero or near-zero

It is known that complete graphs and complete multipartite graphs have modularity zero. We show that the least number of edges we may delete from the complete graph $K_n$ to obtain a graph with non-zero modularity is $\lfloor n/2\rfloor +1$. Similarly we determine the least number of edges we may delete from or add to a complete bipartite graph to reach non-zero modularity. We give some corresponding results for complete multipartite graphs, and a short proof that complete multipartite graphs have modularity zero. We also analyse the modularity of very dense random graphs, and in particular we find that there is a transition to modularity zero when the average degree of the complementary graph drops below 1. Finally we consider some natural variants of the definition of modularity; and investigate which graphs have corresponding modularity value 0, and the least number of edges we may delete from the complete graph $K_n$ to obtain a graph with non-zero modularity.

math.CO↗
arXiv2026

Minimal Construction of Graphs with Maximum Robustness

The notions of $r$-robustness and $(r,s)$-robustness of a network have been earlier introduced in the literature to achieve resilient consensus in the presence of misbehaving agents. However, while higher robustness levels enable networks to tolerate a higher number of misbehaving agents, they also require dense communication structures, which are not always desirable for systems with limited communication ranges, energy, and resources. Therefore, this paper studies the fundamental structures behind $r$-robustness and $(r,s)$- robustness properties in two ways. (a) We first establish tight necessary conditions on the number of edges that an undirected graph with an arbitrary number of nodes must have to achieve maximum $r$- and $(r,s)$-robustness. (b) We then use these conditions to construct two classes of undirected graphs, referred to as $γ$- and $(γ,γ)$-Minimal Edge Robust Graphs (MERGs), that provably achieve maximum robustness with minimal numbers of edges. We demonstrate the effectiveness of our method via comparison against existing robust graph structures and a set of simulations.

eess.SY↗
arXiv2026

Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring

Understanding how higher-order social structures shape epidemic spreading requires models that couple group interactions with adaptive behavior. We introduce an adaptive simplicial susceptible-infected-susceptible (s-SIS) model on d-uniform hypergraphs, where both node states and hyperedge activity co-evolve in response to local infection pressure. Hyperedges represent group interactions of fixed size and dynamically reduce their activity through a feedback mechanism in highly infected environments. Within this framework, we design two classes of hyperedge-level interventions: (i) risk-driven immunization, combining spontaneous, activity-based isolation with targeted deactivation guided by hyperedge infection pressure, and (ii) structural rewiring, which reconstructs group structures either randomly or via degree-preferential attachment. By extending the microscopic Markov chain approximation to higher-order interactions, we derive analytical conditions for the existence and stability of both endemic and disease-free stationary states. Our analysis shows that adaptive hyperedge feedback can induce discontinuous phase transitions, nonlinear epidemic thresholds, and bistable regimes in which sufficiently high initial prevalence drives the system to a disease-free equilibrium. Extensive Monte Carlo simulations support the theory and confirm that targeted immunization and degree-preferential rewiring substantially suppress epidemic prevalence, outperforming random strategies. These results demonstrate that higher-order interactions and adaptive group-level responses fundamentally reshape epidemic bifurcations and suggest principles for designing effective intervention policies in complex social systems.

physics.soc-ph↗
arXiv2021

Detecting the ultra low dimensionality of real networks

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging but necessary to generate efficient embeddings to be used in a multitude of downstream tasks. Here, we propose a method to infer the dimensionality of networks without the need for any a priori spatial embedding. Due to the ability of hyperbolic geometry to capture the complex connectivity of real networks, we detect ultra low dimensionality far below values reported using other approaches. We applied our method to real networks from different domains and found unexpected regularities, including: tissue-specific biomolecular networks being extremely low dimensional; brain connectomes being close to the three dimensions of their anatomical embedding; and social networks and the Internet requiring slightly higher dimensionality. Beyond paving the way towards an ultra efficient dimensional reduction, our findings help address fundamental issues that hinge on dimensionality, such as universality in critical behavior.

physics.soc-ph↗
arXiv2026

Agent-Enhanced Heterogeneous Graph RAG for Academic Question Answering

Academic question answering requires reasoning over heterogeneous scholarly graphs, where queries range from simple attribute lookups to multi-hop inference across author--paper--venue structures. Existing retrieval-augmented generation (RAG) systems struggle in this setting due to three limitations: (1) fixed retrieval strategies that do not adapt to varying query complexity, (2) the absence of sufficiency evaluation leading to incomplete or misaligned evidence, and (3) a lack of structured verification against graph facts. To address these issues, we propose an agentic heterogeneous graph RAG method that transforms the three core stages of the RAG pipeline into explicit agentic decision steps. A query-aware retrieval agent analyzes query type and selects an appropriate graph traversal strategy; a sufficiency-aware reranking agent assesses evidence completeness and adaptively expands the retrieved subgraph; and a graph-grounded verification agent checks entity, relation, and attribute correctness before finalizing the answer. Experiments on heterogeneous graphs constructed from OpenAlex and DBLP suggest that our method consistently outperforms strong LLM, graph-augmented RAG, and agent-based baselines.

cs.SI↗
arXiv2026

Dynamic Heterogeneous Graph Representation Learning: A Survey

Graph representation learning (GRL) serves as a canonical paradigm for modeling complex networks. However, real-world AI systems inherently manifest as evolving heterogeneous entities with complex interactions, posing significant challenges to static or homogeneous modeling. To address these complexities, representation learning for Dynamic Heterogeneous Graphs (DHGs) has emerged as a vital approach for learning low-dimensional representations that simultaneously preserve structural semantics and temporal dynamics. This survey presents the first systematic review of DHG representation learning methods. We first introduce a unified formal definition that encompasses both discrete-time and continuous-time DHGs from the perspective of temporal granularity. Building upon this formulation, we propose a novel algorithm-centric taxonomy that categorizes existing literature, including early embedding-based approaches, graph neural network (GNN)-based models, and relatively recent Transformer-based DHG methods, while explicitly highlighting their intrinsic modeling biases with respect to dynamic granularity. Furthermore, we summarize representative applications of DHG representation learning, along with commonly used datasets and benchmarks. Finally, we discuss promising research directions that guide future advances in this rapidly evolving field.

cs.LG↗
arXiv2026

Statistical Feature Augmentation for Anomaly Detection in Dynamic Graphs

Dynamic networks are being applied in many domains, from social media to logistics systems, each with their own set of special characteristics. A model employed on this type of data must capture the duality between temporal/structural and feature-based information. Yet state-of-the-art deep learning models often struggle to learn especially short-term behavioral interaction signals, such as sender intensity or interaction inertia, directly from raw event streams. To address this gap, we propose a statistical feature augmentation method that explicitly encodes behavioral interaction statistics into the input feature space. We evaluate our proposed method on an anomaly detection task across three real-world datasets (Reddit, Wikipedia, MOOC) and seven models spanning both continuous-time and discrete-time architectures. As a baseline, we apply the same models trained on the original embeddings. Our results show, that augmentation consistently improves detection performance. Beyond performance, the enriched input enables fine-grained post-hoc analysis of behavioral importance, since each statistic occupies a dedicated input dimension. In particular, this work showcases a promising approach for merging classical network analysis with deep learning.

cs.SI↗
arXiv2026

Scalable dynamic community detection on temporal graphs using graph neural networks

Dynamic community detection on temporal graphs seeks to identify evolving community structures while allowing node memberships to change over time. In this work, we formulate dynamic community detection over observed node-time instances, where each node-time instance in the temporal interaction stream is assigned a cluster label. We propose a diffusion-guided contrastive learning framework that uses a local temporal diffusion affinity matrix to construct positive and negative node-time pairs and organise the learned representations according to their temporal structural relationships. We then apply a clustering algorithm to the resulting embedding space to detect dynamic communities. Experiments on synthetic temporal networks show that the proposed method outperforms static community detection baselines and achieves competitive or better performance than existing dynamic community detection methods in terms of AMI and ARI, while maintaining good scalability. We further apply the method to a large-scale OpenAlex computer science collaboration network from 2016 to 2025, revealing persistent and evolving collaboration communities in real scientific data. These results suggest that time-node-level representation learning provides an effective framework for scalable dynamic community detection on temporal graphs.

cs.SI↗
arXiv2026

Polarity-Asymmetric Structural Calibration for Link Sign Prediction

Link sign prediction (LSP) aims to infer the positive or negative polarity of unobserved links in signed networks. Signed Graph Neural Networks (SGNNs) usually rely on signed-graph structural priors, including structural balance and homophily-like similarity, to guide message passing and prediction. These priors describe population-level tendencies, not guarantees for individual target edges. Their failures are especially costly under severe sign imbalance, where errors on minority and locally conflicting relations are harder to detect and correct. We propose Polarity-Asymmetric Structural Calibration (PASC), a target-edge structural-prior calibration framework for signed link prediction. PASC constructs a structure-only prior representation, estimates a target-edge structural prior score, and compares this score with a local signed-context cue to derive a conflict residual. The residual calibrates signed attention aggregation, target-edge gated fusion, and regime-adaptive optimization. Experiments on five real-world signed network datasets show that PASC consistently achieves the best Macro-F1 among representative baselines, with competitive AUC, Binary-F1, and Micro-F1. Structural-shift experiments further suggest reduced dependence on dense-neighborhood and local-closure shortcuts. Source code is available at https://github.com/iqqGGGGGGG/PASC-for-LSP.

cs.SI↗
arXiv2026

Hierarchical Possession-Aware Graph Pointer Network for Pass Receiver Selection

Pass receiver selection is a fundamental task in football analytics, aiming to predict the intended receiver under a given game state. This task is challenging with event-centered freeze-frame observations, a broadcast-like setting that provides only partial and variable player visibility without complete trajectories or stable player identities. The model must therefore reason over anonymous visible candidates, opponent pressure, and recent context under partial observation. To address this setting, we propose a Hierarchical Possession-aware Graph Pointer Network (HPGPN), which formulates pass receiver selection as variable-size candidate prediction over visible teammates. HPGPN jointly models current player interactions, local event context, and possession-level temporal dynamics. It represents the current pass situation with a graph, incorporates fixed event context, and uses dynamic possession history to capture how the attacking sequence evolves. Candidate representations are refined hierarchically by integrating spatial, contextual, and historical evidence, and a glimpse pointer head scores the receiver candidates. Experiments on public football event and freeze-frame data show that HPGPN improves pass receiver selection performance. Ablation studies demonstrate the effectiveness of graph-based interaction modeling, fixed event context, and dual-branch dynamic possession-history modeling.

cs.AI↗