arXiv subjects

Zhongzhi Zhang

Publications and source records attributed to Zhongzhi Zhang.

At least 19 recordsLinked to original sources

arXiv2026

GLIP: Graph and LLM Joint Pretraining for Graph-Level Tasks

Graphs are widely used to model relational systems, with applications in domains such as social networks, finance, and biomedicine. Graph neural networks (GNNs) have become a mainstream approach for learning graph representations. With the rise of large language models (LLMs), recent studies have attempted to combine GNNs with LLMs. However, most existing works concentrate on node-level and edge-level tasks, while graph-level tasks, which require capturing more complex structural and feature information, remain relatively underexplored. Moreover, graph pretraining is a widely adopted strategy to alleviate the challenge of label scarcity. Most existing approaches are designed solely for GNNs such as GraphCL, leaving LLMs uninvolved in the process. To address these limitations, we propose GLIP, a Graph-LLM JoInt Pretraining framework for graph-level tasks. GLIP first performs graph augmentation to construct positive and negative pairs and introduces a multi-token selection strategy to identify patches informative in both structure and features. It further leverages a diffusion-based projector to enrich them with contextual information, enabling GLIP to capture signals from both global and local perspectives. Finally, GLIP employs a joint objective that integrates the LLM's semantic judgments with a contrastive alignment loss, ensuring consistent supervision at both the semantic and structural levels. After pretraining, GLIP is fine-tuned with limited labeled data for downstream tasks, and extensive experiments show that it outperforms state-of-the-art methods on graph-level classification and reasoning tasks. Our source code is publicly available at https://anonymous.4open.science/r/GLIP.

cs.LG↗

arXiv2026

Efficient Computation for Diagonal of Forest Matrix via Variance-Reduced Forest Sampling

The forest matrix of a graph, particularly its diagonal elements, has far-reaching implications in network science and machine learning. The state-of-the-art algorithms for the diagonal of forest matrix computation are based on the fast Laplacian solver. However, these algorithms encounter limitations when applied to digraphs due to the incapacity of the Laplacian solver. To overcome the issue, in this paper, we propose three novel sampling-based algorithms: SCF, SCFV, and SCFV+. Our first algorithm SCF leverages a probability interpretation of the diagonal of the forest matrix and utilizes an extension of Wilson's algorithm to sample spanning converging forests. To reduce the variance in forest sampling, we develop two novel variance-reduction techniques. The first technique, leading to the SCFV algorithm, is inspired by opinion dynamics in graphs and applies matrix-vector iteration to spanning forest sampling. While SCFV achieves reduced variance compared to SCF, the cross-product term in its variance expression can be complex and potentially large in certain graphs. Therefore, we develop another technique, leading to a new iteration equation and the SCFV+ algorithm. SCFV+ achieves further reduced variance without the cross-product term in the variance of SCFV. We prove that SCFV+ can achieve a relative error guarantee with high probability and maintain linear time complexity relative to the number of nodes in the graph, presenting a superior theoretical result compared to state-of-the-art algorithms. Finally, we conduct extensive experiments on various real-world networks, showing that our algorithms achieve better estimation accuracy and are more time-efficient than the state-of-the-art algorithms. Particularly, our algorithms are scalable to massive graphs with more than twenty million nodes in both undirected and directed graphs.

cs.SI↗

arXiv2026

Fast Computation and Optimization for Opinion-Based Quantities of Friedkin-Johnsen Model

In this paper, we address the problem of fast computation and optimization of opinion-based quantities in the Friedkin-Johnsen (FJ) model. We first introduce the concept of partial rooted forests, based on which we present an efficient algorithm for computing relevant quantities using this method. Furthermore, we study two optimization problems in the FJ model: the Opinion Minimization Problem and the Polarization and Disagreement Minimization Problem. For both problems, we propose fast algorithms based on partial rooted forest samplings. Our methods reduce the time complexity from linear to sublinear. Extensive experiments on real-world networks demonstrate that our algorithms are both accurate and efficient, outperforming state-of-the-art methods and scaling effectively to large-scale networks.

cs.SI↗

arXiv2026

Fast Estimation for Forest Matrix of Signed Graphs

The forest matrix of a signed graph plays an important role in network science and social opinion dynamics, yet existing algorithms are mainly designed for unsigned graphs and are difficult to extend to signed graphs. In this paper, we study the problem of efficiently estimating the forest matrix of signed graphs with n nodes and introduce the signed forest matrix theorem, which establishes the relationship between generalized spanning converging forests and the forest matrix. Based on this result, we propose a novel algorithm GSCF, built on a variant of loop-erased random walks, to generate generalized spanning converging forests in expected O(n) time. We further develop two sampling algorithms, FMDE and FMDE+, for estimating the diagonal of the forest matrix, both with time complexity O(ln), where l is the number of samples. Extensive experiments on various signed graphs show that our methods achieve high estimation accuracy, significantly improve computational efficiency, and scale to graphs with over twenty million nodes. Our source code is publicly available on https://github.com/HaoxinSun98/SignedForestDiagonal.

cs.SI↗

arXiv2026

Minimizing Total Biharmonic Distance in Large Graphs via Link Recommendation

The total biharmonic distance, which is the sum of the biharmonic distance between every pair of nodes in a network, is a key metric for evaluating network connectivity and robustness. In this paper, we study the problem of minimizing the total biharmonic distance by adding $k$ nonexistent edges for a given graph $G$ and budget $k$. The problem is computationally challenging. We show that the objective function of the problem is monotone but not supermodular. To solve this problem, we propose simple greedy algorithms with cubic time complexity. To mitigate the high time complexity of these greedy algorithms, we apply several techniques, including the projection method, the Laplacian solver, and convex hull approximation. These techniques reduce the time complexity of our proposed algorithms from cubic to nearly linear while providing error guarantees. Finally, extensive experiments on real datasets demonstrate both the efficiency and effectiveness of our proposed algorithms.

cs.SI↗

arXiv2026

Behavior and Sublinear Algorithm for Opinion Disagreement on Noisy Social Networks

The phenomenon of opinion disagreement has been empirically observed and reported in the literature, which is affected by various factors, such as the structure of social networks. An important discovery in network science is that most real-life networks, including social networks, are scale-free and sparse. In this paper, we study noisy opinion dynamics in sparse scale-free social networks to uncover the influence of power-law topology on opinion disagreement. We adopt the popular discrete-time DeGroot model for opinion dynamics in a graph, where nodes' opinions are subject to white noise. We first study opinion disagreement in many realistic and model networks with a scale-free topology, which approaches a constant, indicating that a scale-free structure is resistant to noise in the opinion dynamics. Moreover, existing algorithms for estimating opinion disagreement are computationally impractical for large-scale networks due to their high computational complexity. To solve this challenge, we introduce a sublinear-time algorithm to approximate this quantity with a theoretically guaranteed error. This algorithm efficiently simulates truncated random walks starting from a subset of nodes while preserving accurate estimation. Extensive experiments demonstrate its efficiency, accuracy, and scalability.

cs.SI↗

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↗

arXiv2026

ProbeWalk: Fast Estimation of Biharmonic Distance on Graphs via Probe-Driven Random Walks

The biharmonic distance is a fundamental metric on graphs that measures the dissimilarity between two nodes, capturing both local and global structures. It has found applications across various fields, including network centrality, graph clustering, and machine learning. These applications typically require efficient evaluation of pairwise biharmonic distances. However, existing algorithms remain computationally expensive. The state-of-the-art method attains an absolute-error guarantee epsilon_abs with time complexity O(L^5 / epsilon_abs^2), where L denotes the truncation length. In this work, we improve the complexity to O(L^3 / epsilon^2) under a relative-error guarantee epsilon via probe-driven random walks. We provide a relative-error guarantee rather than an absolute-error guarantee because biharmonic distances vary by orders of magnitude across node pairs. Since L is often very large in real-world networks (for example, L >= 10^3), reducing the L-dependence from the fifth to the third power yields substantial gains. Extensive experiments on real-world networks show that our method delivers 10x-1000x per-query speedups at matched relative error over strong baselines and scales to graphs with tens of millions of nodes.

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

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

Opinion Maximization in Social Networks by Modifying Internal Opinions

Public opinion governance in social networks is critical for public health campaigns, political elections, and commercial marketing. In this paper, we addresse the problem of maximizing overall opinion in social networks by strategically modifying the internal opinions of key nodes. Traditional matrix inversion methods suffer from prohibitively high computational costs, prompting us to propose two efficient sampling-based algorithms. Furthermore, we develop a deterministic asynchronous algorithm that exactly identifies the optimal set of nodes through asynchronous update operations and progressive refinement, ensuring both efficiency and precision. Extensive experiments on real-world datasets demonstrate that our methods outperform baseline approaches. Notably, our asynchronous algorithm delivers exceptional efficiency and accuracy across all scenarios, even in networks with tens of millions of nodes.

cs.SI↗

arXiv2025

Efficient Algorithms for Relevant Quantities of Friedkin-Johnsen Opinion Dynamics Model

Online social networks have become an integral part of modern society, profoundly influencing how individuals form and exchange opinions across diverse domains ranging from politics to public health. The Friedkin-Johnsen model serves as a foundational framework for modeling opinion formation dynamics in such networks. In this paper, we address the computational task of efficiently determining the equilibrium opinion vector and associated metrics including polarization and disagreement, applicable to both directed and undirected social networks. We propose a deterministic local algorithm with relative error guarantees, scaling to networks exceeding ten million nodes. Further acceleration is achieved through integration with successive over-relaxation techniques, where a relaxation factor optimizes convergence rates. Extensive experiments on diverse real-world networks validate the practical effectiveness of our approaches, demonstrating significant improvements in computational efficiency and scalability compared to conventional methods.

cs.SI↗

arXiv2025

Fast Maximization of Current Flow Group Closeness Centrality

Derived from effective resistances, the current flow closeness centrality (CFCC) for a group of nodes measures the importance of node groups in an undirected graph with $n$ nodes. Given the widespread applications of identifying crucial nodes, we investigate the problem of maximizing CFCC for a node group $S$ subject to the cardinality constraint $|S|=k\ll n$. Despite the proven NP-hardness of this problem, we propose two novel greedy algorithms for its solution. Our algorithms are based on spanning forest sampling and Schur complement, which exhibit nearly linear time complexities and achieve an approximation factor of $1-\frac{k}{k-1}\frac{1}{\mathrm{e}}-ε$ for any $0<ε<1$. Extensive experiments on real-world graphs illustrate that our algorithms outperform the state-of-the-art method in terms of efficiency and effectiveness, scaling to graphs with millions of nodes.

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↗

arXiv2024

Means of Hitting Times for Random Walks on Graphs: Connections, Computation, and Optimization

For random walks on graph $\mathcal{G}$ with $n$ vertices and $m$ edges, the mean hitting time $H_j$ from a vertex chosen from the stationary distribution to vertex $j$ measures the importance for $j$, while the Kemeny constant $\mathcal{K}$ is the mean hitting time from one vertex to another selected randomly according to the stationary distribution. In this paper, we first establish a connection between the two quantities, representing $\mathcal{K}$ in terms of $H_j$ for all vertices. We then develop an efficient algorithm estimating $H_j$ for all vertices and $\mathcal{K}$ in nearly linear time of $m$. Moreover, we extend the centrality $H_j$ of a single vertex to $H(S)$ of a vertex set $S$, and establish a link between $H(S)$ and some other quantities. We further study the NP-hard problem of selecting a group $S$ of $k\ll n$ vertices with minimum $H(S)$, whose objective function is monotonic and supermodular. We finally propose two greedy algorithms approximately solving the problem. The former has an approximation factor $(1-\frac{k}{k-1}\frac{1}{e})$ and $O(kn^3)$ running time, while the latter returns a $(1-\frac{k}{k-1}\frac{1}{e}-ε)$-approximation solution in nearly-linear time of $m$, for any parameter $0<ε<1$. Extensive experiment results validate the performance of our algorithms.

cs.SI↗

arXiv2024

Fast Computation for the Forest Matrix of an Evolving Graph

The forest matrix plays a crucial role in network science, opinion dynamics, and machine learning, offering deep insights into the structure of and dynamics on networks. In this paper, we study the problem of querying entries of the forest matrix in evolving graphs, which more accurately represent the dynamic nature of real-world networks compared to static graphs. To address the unique challenges posed by evolving graphs, we first introduce two approximation algorithms, \textsc{SFQ} and \textsc{SFQPlus}, for static graphs. \textsc{SFQ} employs a probabilistic interpretation of the forest matrix, while \textsc{SFQPlus} incorporates a novel variance reduction technique and is theoretically proven to offer enhanced accuracy. Based on these two algorithms, we further devise two dynamic algorithms centered around efficiently maintaining a list of spanning converging forests. This approach ensures $O(1)$ runtime complexity for updates, including edge additions and deletions, as well as for querying matrix elements, and provides an unbiased estimation of forest matrix entries. Finally, through extensive experiments on various real-world networks, we demonstrate the efficiency and effectiveness of our algorithms. Particularly, our algorithms are scalable to massive graphs with more than forty million nodes.

cs.SI↗

arXiv2024

Fast Computation of Kemeny's Constant for Directed Graphs

Kemeny's constant for random walks on a graph is defined as the mean hitting time from one node to another selected randomly according to the stationary distribution. It has found numerous applications and attracted considerable research interest. However, exact computation of Kemeny's constant requires matrix inversion, which scales poorly for large networks with millions of nodes. Existing approximation algorithms either leverage properties exclusive to undirected graphs or involve inefficient simulation, leaving room for further optimization. To address these limitations for directed graphs, we propose two novel approximation algorithms for estimating Kemeny's constant on directed graphs with theoretical error guarantees. Extensive numerical experiments on real-world networks validate the superiority of our algorithms over baseline methods in terms of efficiency and accuracy.

cs.SI↗

arXiv2024

Fast Query of Biharmonic Distance in Networks

The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's importance, efficient algorithms for the exact computation or approximation of this metric on large graphs remain notably absent. In this work, we provide several algorithms to estimate BD, building on a novel formulation of this metric. These algorithms enjoy locality property (that is, they only read a small portion of the input graph) and at the same time possess provable performance guarantees. In particular, our main algorithms approximate the BD between any node pair with an arbitrarily small additive error $\eps$ in time $O(\frac{1}{\eps^2}\text{poly}(\log\frac{n}{\eps} ))$. Furthermore, we perform an extensive empirical study on several benchmark networks, validating the performance and accuracy of our algorithms.

cs.SI↗