Zonghan Zhang

Zijian Zhang, Zonghan Zhang, Zhiqian Chen

The occurrence of diffusion on a graph is a prevalent and significant phenomenon, as evidenced by the spread of rumors, influenza-like viruses, smart grid failures, and similar events. Comprehending the behaviors of flow is a formidable task, due to the intricate interplay between the distribution of seeds that initiate flow propagation, the propagation model, and the topology of the graph. The study of networks encompasses a diverse range of academic disciplines, including mathematics, physics, social science, and computer science. This interdisciplinary nature of network research is characterized by a high degree of specialization and compartmentalization, and the cooperation facilitated by them is inadequate. From a machine learning standpoint, there is a deficiency in a cohesive platform for assessing algorithms across various domains. One of the primary obstacles to current research in this field is the absence of a comprehensive curated benchmark suite to study the flow behaviors under network scenarios. To address this disparity, we propose the implementation of a novel benchmark suite that encompasses a variety of tasks, baseline models, graph datasets, and evaluation tools. In addition, we present a comprehensive analytical framework that offers a generalized approach to numerous flow-related tasks across diverse domains, serving as a blueprint and roadmap. Drawing upon the outcomes of our empirical investigation, we analyze the advantages and disadvantages of current foundational models, and we underscore potential avenues for further study. The datasets, code, and baseline models have been made available for the public at: https://github.com/XGraphing/XFlow

Zonghan Zhang, Zhiqian Chen

Given its vast application on online social networks, Influence Maximization (IM) has garnered considerable attention over the last couple of decades. Due to the intricacy of IM, most current research concentrates on estimating the first-order contribution of the nodes to select a seed set, disregarding the higher-order interplay between different seeds. Consequently, the actual influence spread frequently deviates from expectations, and it remains unclear how the seed set quantitatively contributes to this deviation. To address this deficiency, this work dissects the influence exerted on individual seeds and their higher-order interactions utilizing the Sobol index, a variance-based sensitivity analysis. To adapt to IM contexts, seed selection is phrased as binary variables and split into distributions of varying orders. Based on our analysis with various Sobol indices, an IM algorithm dubbed SIM is proposed to improve the performance of current IM algorithms by over-selecting nodes followed by strategic pruning. A case study is carried out to demonstrate that the explanation of the impact effect can dependably identify the key higher-order interactions among seeds. SIM is empirically proved to be superior in effectiveness and competitive in efficiency by experiments on synthetic and real-world graphs.

Zonghan Zhang, Zijian Zhang, Zhiqian Chen

Due to the significance of its various applications, source localization has garnered considerable attention as one of the most important means to confront diffusion hazards. Multi-source localization from a single-snapshot observation is especially relevant due to its prevalence. However, the inherent complexities of this problem, such as limited information, interactions among sources, and dependence on diffusion models, pose challenges to resolution. Current methods typically utilize heuristics and greedy selection, and they are usually bonded with one diffusion model. Consequently, their effectiveness is constrained. To address these limitations, we propose a simulation-based method termed BOSouL. Bayesian optimization (BO) is adopted to approximate the results for its sample efficiency. A surrogate function models uncertainty from the limited information. It takes sets of nodes as the input instead of individual nodes. BOSouL can incorporate any diffusion model in the data acquisition process through simulations. Empirical studies demonstrate that its performance is robust across graph structures and diffusion models. The code is available at https://github.com/XGraph-Team/BOSouL.

Zhiqian Chen, Zonghan Zhang

Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the effect of graph topology and node features on performance, and are even surpassed by some models that do not consider graph structure or node properties. We quantify the information overlap between graph topology, node features, and labels in order to determine graph convolution's representation power in the node classification task. In this work, we first determine the linear separability of graph convoluted features using analysis of variance. Mutual information is used to acquire a better understanding of the possible non-linear relationship between graph topology, node features, and labels. Our theoretical analysis demonstrates that a simple and efficient graph operation that concatenates only graph topology and node properties consistently outperforms conventional graph convolution, especially in the heterophily case. Extensive empirical research utilizing a synthetic dataset and real-world benchmarks demonstrates that graph concatenation is a simple but more flexible alternative to graph convolution.