arXiv subjects

Ahad N. Zehmakan

Publications and source records attributed to Ahad N. Zehmakan.

At least 19 recordsLinked to original sources

arXiv2026

Polarization Dynamics under Algorithmic Recommendations in LLM-based Online Social Networks

How do recommendation algorithms contribute to the formation of polarized opinions in online social networks? This question has been studied through empirical analyses of real platforms and mathematical models of opinion dynamics. Empirical studies capture user behavior but are often limited by noisy, incomplete, or inaccessible platform data, while mathematical models offer control and interpretability but usually rely on simplified opinion update rules. More recently, large language model (LLM)-based social simulations have provided an alternative for studying recommendation and opinion dynamics through natural-language interactions. However, how different ways of applying recommendations shape opinion dynamics remains underexplored. In this work, we provide a controlled comparison of two different recommendation mechanisms in an LLM-based online social network simulation. Edge Recommendation (ER) introduces new connections in the network, while Content-Exposure Recommendation (CR) exposes additional users to individual posts without modifying the underlying graph. Our framework represents users as LLM-based agents who interact in natural language while maintaining evolving opinion states. We measure polarization as opinion dispersion, extremization as the average distance of opinions from the neutral midpoint, and reinforcement as interactions that amplify already aligned opinions. Our results show higher mean polarization and extremization across recommendation conditions compared with the no-recommendation baseline, with absolute differences of up to $0.12$ in our main experiments.

cs.SI↗

arXiv2026

Distilling Graph Geometry: Knowledge Gap from GNNs to MLPs

GNN-to-MLP distillation aims to retain the predictive accuracy of a message-passing teacher while deploying a graph-free MLP at inference. Existing methods mainly transfer node-wise predictions or use confidence-based reweighting, but they do not specify where the student should preserve the teacher's graph-induced geometry. We show that this omission leads to two spectral failure modes in the student's representation space. On sparse graphs, the student suffers from spectral underfit, missing high-energy teacher directions concentrated near boundary regions. On dense graphs, it suffers from spectral overfit, retaining spurious directions that the teacher has collapsed through aggregation. Motivated by an energy-weighted teacher-student alignment objective, we propose Graph Geometry-aware MLP (G^2MLP), a training-time distillation framework guided by Ollivier-Ricci curvature. Curvature identifies where the two spectral errors concentrate and is used to allocate supervision between prediction-level and representation-level alignment. The deployed model remains a standard MLP and requires no graph access at inference. Across node-classification benchmarks, G^2MLP consistently improves over graph-free distillation baselines, reduces the teacher-student rank gap in both regimes, and transfers without architectural changes to Graph Transformer teachers and link prediction.

cs.LG↗

arXiv2026

Quantifying and Minimizing Perception Gap in Social Networks

Social media has transformed global communication, yet its network structure can systematically distort perceptions through effects like the majority illusion and echo chambers. We introduce the perception gap index, a graph-based measure that quantifies local-global opinion divergence, which can be viewed as a generalization of the majority illusion to continuous settings. Using techniques from spectral graph theory, we demonstrate that higher connectivity makes networks more resilient to perception distortion. Our analysis of stochastic block models, however, shows that pronounced community structure increases vulnerability. We also study the problem of minimizing the perception gap via link recommendation with a fixed budget. We prove that this problem does not admit a polynomial-time algorithm for any bounded approximation ratio, unless P = NP. However, we propose a collection of efficient heuristic methods that have been demonstrated to produce near-optimal solutions on real-world network data.

cs.SI↗

arXiv2026

Not Just Oversmoothing: Detecting the Echo Chamber Effect in Graph Neural Networks

Oversmoothing is a well-known failure mode of Graph Neural Networks (GNNs). However, most existing diagnostics rely on global aggregation measures that fail to capture the heterogeneous dynamics of message passing. Real-world graphs exhibit pronounced community structure, and message passing operates on two timescales, with representations collapsing rapidly within communities and slowly across them. This creates a critical gap in which intra-community representations can become indistinguishable while inter community separation persists, a failure mode that we refer to as the Echo Chamber Effect. To quantify this effect, we introduce the Echo Chamber Index (ECI), which stratifies pairwise distances by community membership and reveals when global energy diminishes while inter-community separation persists. ECI further shows that feature retention mechanisms can preserve the echo chamber under the conditions of our theoretical analysis. The consequences depend on label structure: when communities align with classes, the echo chamber can sharpen node classification, whereas when they do not, the same collapse makes classification provably harder. Motivated by this analysis, we propose Community-Aware Split Propagation (CASP), a lightweight plugin that decouples intra- and inter-community aggregation and learns their balance from label structure. CASP improves diverse backbone GNNs across most evaluated homophilic and heterophilic settings.

cs.LG↗

arXiv2026

JECHO: Scalable Echo Chamber Detection via Jaccard-based Homophily and Seed Expansion

Detecting echo chambers is critical for understanding and limiting negative social phenomena, such as online polarization, misinformation, and conspiracy theory diffusion. However, the echo chamber detection (ECD) problem yet lacks a rigorous algorithmic foundation. We address this gap by formalizing a unified definition of echo chambers based on three principles: internal opinion homogeneity, opinion extremism, and structural isolation. Under such a definition, we establish the theoretical hardness of the ECD problem, proving it is NP-hard via a reduction from the conductance minimization problem. To circumvent this computational barrier, we derive a theoretical lower bound on the Jaccard-based homophily (JHO) of nodes that reside within valid echo chambers. This guarantee motivates JECHO, a novel algorithm that detects echo chambers via local seed expansion rather than global enumeration. JECHO first identifies seeds that exceed the JHO threshold and then applies a score-based expansion to optimize structural isolation. Extensive experiments on real-world and synthetic networks demonstrate that our theory-guided approach detects more structurally isolated echo chambers than state-of-the-art methods while reducing runtime by orders of magnitude.

cs.SI↗

arXiv2026

Opinion Polarization in LLM-Based Social Networks: Manipulation and Mitigation

How vulnerable are online social networks to adversaries who seek to amplify opinion polarization by manipulating opinions, and how difficult is it to mitigate such manipulation? Existing studies have examined this question using mathematical models of opinion dynamics. While these models offer valuable theoretical insights, they rely on simplified assumptions about interactions, message content, and opinion updates, limiting the adversarial strategies they can capture and the applicability of their findings to real-world settings. Large language model (LLM)-based simulations provide a richer alternative: agents can be assigned diverse personas, communicate through natural language, and respond to persuasive or adversarial content in a context-dependent way. This enables the study of manipulation strategies that are difficult to represent using classical mathematical models. To the best of our knowledge, this study provides the first systematic analysis of polarization amplification and mitigation in an LLM-based simulated social network framework. In our framework, LLM agents with diverse personas interact over a social network by exchanging natural language posts and updating their opinions accordingly. We show that even an adversary with a limited manipulation budget can considerably increase polarization. We then study two classes of defense mechanisms: reactive mitigations, which assign specific users to actively counter manipulation, and proactive interventions, which increase resistance through general mechanisms not tied to particular users. Our results show that although these mechanisms reduce the impact of adversarial attacks, they generally do not restore the network to its baseline polarization state. These findings suggest that neither approach fully overcomes the vulnerability of the network, highlighting the potential risk of such attacks.

cs.SI↗

arXiv2026

Invariant-Stratified Propagation for Expressive Graph Neural Networks

Graph Neural Networks (GNNs) face fundamental limitations in expressivity and capturing structural heterogeneity. Standard message-passing architectures are constrained by the 1-dimensional Weisfeiler-Leman (1-WL) test, unable to distinguish graphs beyond degree sequences, and aggregate information uniformly from neighbors, failing to capture how nodes occupy different structural positions within higher-order patterns. While methods exist to achieve higher expressivity, they incur prohibitive computational costs and lack unified frameworks for flexibly encoding diverse structural properties. To address these limitations, we introduce Invariant-Stratified Propagation (ISP), a framework comprising both a novel WL variant (ISP-WL) and its efficient neural network implementation (ISPGNN). ISP stratifies nodes according to graph invariants, processing them in hierarchical strata that reveal structural distinctions invisible to 1-WL. Through hierarchical structural heterogeneity encoding, ISP quantifies differences in nodes' structural positions within higher-order patterns, distinguishing interactions where participants occupy different roles from those with uniform participation. We provide formal theoretical analysis establishing enhanced expressivity beyond 1-WL, convergence guarantees, and inherent resistance to oversmoothing. Extensive experiments across graph classification, node classification, and influence estimation demonstrate consistent improvements over standard architectures and state-of-the-art expressive baselines.

cs.LG↗

arXiv2026

Efficient Edge Rewiring Strategies for Enhancing PageRank Fairness

We study the notion of unfairness in social networks, where a group such as females in a male-dominated industry are disadvantaged in access to important information, e.g. job posts, due to their less favorable positions in the network. We investigate a well-established network-based formulation of fairness called PageRank fairness, which refers to a fair allocation of the PageRank weights among distinct groups. Our goal is to enhance the PageRank fairness by modifying the underlying network structure. More precisely, we study the problem of maximizing PageRank fairness with respect to a disadvantaged group, when we are permitted to rewire a fixed number of edges in the network. Building on a greedy approach, we leverage techniques from fast sampling of rooted spanning forests to devise an effective linear-time algorithm for this problem. To evaluate the accuracy and performance of our proposed algorithm, we conduct a large set of experiments on various real-world network data. Our experiments demonstrate that the proposed algorithm significantly outperforms the existing ones. Our algorithm is capable of generating accurate solutions for networks of million nodes in just a few minutes.

cs.SI↗

arXiv2025

Promoting Fairness in Information Access within Social Networks

The advent of online social networks has facilitated fast and wide spread of information. However, some users, especially members of minority groups, may be less likely to receive information spreading on the network, due to their disadvantaged network position. We study the optimization problem of adding new connections to a network to enhance fairness in information access among different demographic groups. We provide a concrete formulation of this problem where information access is measured in terms of resistance distance, {offering a new perspective that emphasizes global network structure and multi-path connectivity.} The problem is shown to be NP-hard. We propose a simple greedy algorithm which turns out to output accurate solutions, but its run time is cubic, which makes it undesirable for large networks. As our main technical contribution, we reduce its time complexity to linear, leveraging several novel approximation techniques. In addition to our theoretical findings, we also conduct an extensive set of experiments using both real-world and synthetic datasets. We demonstrate that our linear-time algorithm can produce accurate solutions for networks with millions of nodes.

cs.SI↗

arXiv2025

Adaptive Initial Residual Connections for GNNs with Theoretical Guarantees

Message passing is the core operation in graph neural networks, where each node updates its embeddings by aggregating information from its neighbors. However, in deep architectures, this process often leads to diminished expressiveness. A popular solution is to use residual connections, where the input from the current (or initial) layer is added to aggregated neighbor information to preserve embeddings across layers. Following a recent line of research, we investigate an adaptive residual scheme in which different nodes have varying residual strengths. We prove that this approach prevents oversmoothing; particularly, we show that the Dirichlet energy of the embeddings remains bounded away from zero. This is the first theoretical guarantee not only for the adaptive setting, but also for static residual connections (where residual strengths are shared across nodes) with activation functions. Furthermore, extensive experiments show that this adaptive approach outperforms standard and state-of-the-art message passing mechanisms, especially on heterophilic graphs. To improve the time complexity of our approach, we introduce a variant in which residual strengths are not learned but instead set heuristically, a choice that performs as well as the learnable version.

cs.LG↗

arXiv2025

Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily

Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels or properties. While recent work has introduced mechanisms to improve GNN performance under heterophily, certain key limitations still exist. Most existing models apply a fixed aggregation depth across all nodes, overlooking the fact that nodes may require different propagation depths based on their local homophily levels and neighborhood structures. Moreover, many methods are tailored to either homophilic or heterophilic settings, lacking the flexibility to generalize across both regimes. To address these challenges, we develop a theoretical framework that links local structural and label characteristics to information propagation dynamics at the node level. Our analysis shows that optimal aggregation depth varies across nodes and is critical for preserving class-discriminative information. Guided by this insight, we propose a novel adaptive-depth GNN architecture that dynamically selects node-specific aggregation depths using theoretically grounded metrics. Our method seamlessly adapts to both homophilic and heterophilic patterns within a unified model. Extensive experiments demonstrate that our approach consistently enhances the performance of standard GNN backbones across diverse benchmarks.

cs.LG↗

arXiv2025

Opinion Dynamics: A Comprehensive Overview

Opinion dynamics, the evolution of individuals through social interactions, is an important area of research with applications ranging from politics to marketing. Due to its interdisciplinary relevance, studies of opinion dynamics remain fragmented across computer science, mathematics, the social sciences, and physics, and often lack shared frameworks. This survey bridges these gaps by reviewing well-known models of opinion dynamics within a unified framework and categorizing them into distinct classes based on their properties. Furthermore, the key findings on these models are covered in three parts: convergence properties, viral marketing, and user characteristics. We first analyze the final configuration (consensus vs polarized) and convergence time for each model. We then review the main algorithmic, complexity, and combinatorial results in the context of viral marketing. Finally, we explore how node characteristics, such as stubbornness, activeness, or neutrality, shape diffusion outcomes. By unifying terminology, methods, and challenges across disciplines, this paper aims to foster cross-disciplinary collaboration and accelerate progress in understanding and harnessing opinion dynamics.

cs.SI↗

arXiv2025

Efficient Algorithms for Computing Random Walk Centrality

Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph structural information and its wide range of applications, computing this measure for large networks remains impractical due to the computational demands of existing methods. In this paper, we present a novel formulation of random walk centrality, underpinning two scalable algorithms: one leveraging approximate Cholesky factorization and sparse inverse estimation, while the other sampling rooted spanning trees. Both algorithms operate in near-linear time and provide strong approximation guarantees. Extensive experiments on large real-world networks, including one with over 10 million nodes, demonstrate the efficiency and approximation quality of the proposed algorithms.

cs.AI↗

arXiv2025

Graph Neural Diffusion via Generalized Opinion Dynamics

There has been a growing interest in developing diffusion-based Graph Neural Networks (GNNs), building on the connections between message passing mechanisms in GNNs and physical diffusion processes. However, existing methods suffer from three critical limitations: (1) they rely on homogeneous diffusion with static dynamics, limiting adaptability to diverse graph structures; (2) their depth is constrained by computational overhead and diminishing interpretability; and (3) theoretical understanding of their convergence behavior remains limited. To address these challenges, we propose GODNF, a Generalized Opinion Dynamics Neural Framework, which unifies multiple opinion dynamics models into a principled, trainable diffusion mechanism. Our framework captures heterogeneous diffusion patterns and temporal dynamics via node-specific behavior modeling and dynamic neighborhood influence, while ensuring efficient and interpretable message propagation even at deep layers. We provide a rigorous theoretical analysis demonstrating GODNF's ability to model diverse convergence configurations. Extensive empirical evaluations of node classification and influence estimation tasks confirm GODNF's superiority over state-of-the-art GNNs.

cs.LG↗

arXiv2025

Graph-based Fake Account Detection: A Survey

In recent years, there has been a growing effort to develop effective and efficient algorithms for fake account detection in online social networks. This survey comprehensively reviews existing methods, with a focus on graph-based techniques that utilise topological features of social graphs (in addition to account information, such as their shared contents and profile data) to distinguish between fake and real accounts. We provide several categorisations of these methods (for example, based on techniques used, input data, and detection time), discuss their strengths and limitations, and explain how these methods connect in the broader context. We also investigate the available datasets, including both real-world data and synthesised models. We conclude the paper by proposing several potential avenues for future research.

cs.SI↗

arXiv2025

A Generalisation of Voter Model: Influential Nodes and Convergence Properties

Consider an undirected graph G, representing a social network, where each node is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at random and adopts its colour. Despite its significant popularity, this model does not capture some fundamental real-world characteristics such as the difference in the strengths of individuals connections, individuals with neutral opinion on a topic, and individuals who are reluctant to update their opinion. To address these issues, we introduce and study a generalisation of the voter model. Motivating by campaigning strategies, we study the problem of selecting a set of seeds blue nodes to maximise the expected number of blue nodes after some rounds. We prove that the problem is NP- hard and provide a polynomial time approximation algorithm with the best possible approximation guarantee. Our experiments on real-world and synthetic graph data demonstrate that the proposed algorithm outperforms other algorithms. We also investigate the convergence properties of the model. We prove that the process could take an exponential number of rounds to converge. However, if we limit ourselves to strongly connected graphs, the convergence time is polynomial and the period (the number of states in convergence) divides the length of all cycles in the graph.

cs.SI↗

arXiv2025

The Impact of External Sources on the Friedkin-Johnsen Model

To obtain a foundational understanding of timeline algorithms and viral content in shaping public opinions, computer scientists started to study augmented versions of opinion formation models from sociology. In this paper, we generalize the popular Friedkin--Johnsen model to include the effects of external media sources on opinion formation. Our goal is to mathematically analyze the influence of biased media, arising from factors such as manipulated news reporting or the phenomenon of false balance. Within our framework, we examine the scenario of two opposing media sources, which do not adapt their opinions like ordinary nodes, and analyze the conditions and the number of periods required for radicalizing the opinions in the network. When both media sources possess equal influence, we theoretically characterize the final opinion configuration. In the special case where there is only a single media source present, we prove that media sources which do not adapt their opinions are significantly more powerful than those which do. Lastly, we conduct the experiments on real-world and synthetic datasets, showing that our theoretical guarantees closely align with experimental simulations.

cs.SI↗

arXiv2025

Efficient Algorithms for Minimizing the Kirchhoff Index via Adding Edges

The Kirchhoff index, which is the sum of the resistance distance between every pair of nodes in a network, is a key metric for gauging network performance, where lower values signify enhanced performance. In this paper, we study the problem of minimizing the Kirchhoff index by adding edges. We first provide a greedy algorithm for solving this problem and give an analysis of its quality based on the bounds of the submodularity ratio and the curvature. Then, we introduce a gradient-based greedy algorithm as a new paradigm to solve this problem. To accelerate the computation cost, we leverage geometric properties, convex hull approximation, and approximation of the projected coordinate of each point. To further improve this algorithm, we use pre-pruning and fast update techniques, making it particularly suitable for large networks. Our proposed algorithms have nearly-linear time complexity. We provide extensive experiments on ten real networks to evaluate the quality of our algorithms. The results demonstrate that our proposed algorithms outperform the state-of-the-art methods in terms of efficiency and effectiveness. Moreover, our algorithms are scalable to large graphs with over 5 million nodes and 12 million edges.

cs.DM↗