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Graph partitioning (GP) is a classic problem that divides the node set of a graph into densely-connected blocks. Following the IEEE HPEC Graph Challenge and recent advances in pre-training techniques (e.g., large-language models), we propose PR-GPT (Pre-trained & Refined Graph ParTitioning) based on a novel pre-training & refinement paradigm. We first conduct the offline pre-training of a deep graph learning (DGL) model on small synthetic graphs with various topology properties. By using the inductive inference of DGL, one can directly generalize the pre-trained model (with frozen model parameters) to large graphs and derive feasible GP results. We also use the derived partition as a good initialization of an efficient GP method (e.g., InfoMap) to further refine the quality of partitioning. In this setting, the online generalization and refinement of PR-GPT can not only benefit from the transfer ability regarding quality but also ensure high inference efficiency without re-training. Based on a mechanism of reducing the scale of a graph to be processed by the refinement method, PR-GPT also has the potential to support streaming GP. Experiments on the Graph Challenge benchmark demonstrate that PR-GPT can ensure faster GP on large-scale graphs without significant quality degradation, compared with running a refinement method from scratch. We will make our code public at https://github.com/KuroginQin/PRGPT., Comment: Champion winner of IEEE HPEC 2024 Graph Challenge (https://graphchallenge.mit.edu/champions)

Community detection (CD) is a classic graph inference task that partitions nodes of a graph into densely connected groups. While many CD methods have been proposed with either impressive quality or efficiency, balancing the two aspects remains a challenge. This study explores the potential of deep graph learning to achieve a better trade-off between the quality and efficiency of K-agnostic CD, where the number of communities K is unknown. We propose PRoCD (Pre-training & Refinement fOr Community Detection), a simple yet effective method that reformulates K-agnostic CD as the binary node pair classification. PRoCD follows a pre-training & refinement paradigm inspired by recent advances in pre-training techniques. We first conduct the offline pre-training of PRoCD on small synthetic graphs covering various topology properties. Based on the inductive inference across graphs, we then generalize the pre-trained model (with frozen parameters) to large real graphs and use the derived CD results as the initialization of an existing efficient CD method (e.g., InfoMap) to further refine the quality of CD results. In addition to benefiting from the transfer ability regarding quality, the online generalization and refinement can also help achieve high inference efficiency, since there is no time-consuming model optimization. Experiments on public datasets with various scales demonstrate that PRoCD can ensure higher efficiency in K-agnostic CD without significant quality degradation., Comment: Accepted by ACM KDD 2024

Network dynamic (e.g., traffic burst in data center networks and channel fading in cellular WiFi networks) has a great impact on the performance of communication networks (e.g., throughput, capacity, delay, and jitter). This article proposes a unified prediction-based method to handle the dynamic of various network systems. From the view of graph deep learning, I generally formulate the dynamic prediction of networks as a temporal link prediction task and analyze the possible challenges of the prediction of weighted networks, where link weights have the wide-value-range and sparsity issues. Inspired by the high-resolution video frame prediction with generative adversarial network (GAN), I try to adopt adversarial learning to generate high-quality predicted snapshots for network dynamic, which is expected to support the precise and fine-grained network control. A novel high-quality temporal link prediction (HQ-TLP) model with GAN is then developed to illustrate the potential of my basic idea. Extensive experiments for various application scenarios further demonstrate the powerful capability of HQ-TLP.

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved, it can be categorized into the identity and position embedding. However, existing methods can only capture one type of property. Some approaches can support the inductive inference that generalizes the embedding model to new nodes or graphs but relies on the availability of attributes. Due to the complicated correlations between topology and attributes, it is unclear for some inductive methods which type of property they can capture. In this study, we explore a unified framework for the joint inductive inference of identity and position embeddings without attributes. An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk on graph topology and simultaneously derives identity and position embeddings that are jointly optimized. In particular, we demonstrate that some random walk statistics can be informative features to characterize node identities and positions while supporting the inductive embedding inference. Experiments validate the superior performance of IRWE beyond various baselines for the transductive and inductive inference of identity and position embeddings.

Graph partitioning (GP), a.k.a. community detection, is a classic problem that divides the node set of a graph into densely-connected blocks. Following prior work on the IEEE HPEC Graph Challenge benchmark and recent advances in graph machine learning, we propose a novel RAndom FasT Graph Partitioning (RaftGP) method based on an efficient graph embedding scheme. It uses the Gaussian random projection to extract community-preserving features from classic GP objectives. These features are fed into a graph neural network (GNN) to derive low-dimensional node embeddings. Surprisingly, our experiments demonstrate that a randomly initialized GNN even without training is enough for RaftGP to derive informative community-preserving embeddings and support high-quality GP. To enable the derived embeddings to tackle GP, we introduce a hierarchical model selection algorithm that simultaneously determines the number of blocks and the corresponding GP result. We evaluate RaftGP on the Graph Challenge benchmark and compare the performance with five baselines, where our method can achieve a better trade-off between quality and efficiency. In particular, compared to the baseline algorithm of the IEEE HPEC Graph Challenge, our method is 6.68x -- 23.9x faster on graphs with 1E3 -- 5E4 nodes and at least 64.5x faster on larger (1E5 node) graphs on which the baseline takes more than 1E4 seconds. Our method achieves better accuracy on all test cases. We also develop a new graph generator to address some limitations of the original generator in the benchmark.

Graph representation learning (a.k.a. network embedding) is a significant topic of network analysis, due to its effectiveness to support various graph inference tasks. In this paper, we study the representation learning with multiple information sources in attributed graphs. Recent studies usually focus on several specific sources (e.g., high-order proximity and node attributes) but few of them can be extended to incorporate other available sources not specified. In addition, most existing methods assume that all the integrated sources share consistent latent features but may ignore the possible inconsistency among them, lacking the required robustness. To address these issues, we propose a novel adaptive hybrid graph representation (AHGR) method from a view of graph reweighting, where each information source is formulated as a corresponding auxiliary graph, enabling AHGR to integrate arbitrary available information sources. Moreover, a new transition relation among the reweighted graphs is then introduced to perceive and resist the possible inconsistency among multiple sources, enhancing the robustness of AHGR. We verify the effectiveness of AHGR on a series of synthetic and real attributed graphs, where it presents superior performance over other baselines.

In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination of two optimization objectives, we propose a novel semantic graph representation (SGR) method to formulate the joint optimization of the two heterogeneous sources into a common high-order proximity based framework. Concretely, we first construct an auxiliary weighted graph, where the complex homogeneous and heterogeneous relations among nodes and attributes in the original graph are comprehensively encoded. Conventional embedding methods that consider high-order topology proximities can then be easily applied to the newly constructed graph to learn the representations of both node and attribute while capturing the nonlinear high-order intrinsic correlation inside or among graph structure and semantic. The learned attribute embeddings can also effectively support some semantic-oriented inference tasks (e.g., semantic community detection), helping to reveal the graph's deep semantic. The effectiveness of SGR is further verified on a series of real graphs, where it achieves impressive performance over other baselines.

Dynamic graphs serve as a generic abstraction and description of the evolutionary behaviors of various complex systems (e.g., social networks and communication networks). Temporal link prediction (TLP) is a classic yet challenging inference task on dynamic graphs, which predicts possible future linkage based on historical topology. The predicted future topology can be used to support some advanced applications on real-world systems (e.g., resource pre-allocation) for better system performance. This survey provides a comprehensive review of existing TLP methods. Concretely, we first give the formal problem statements and preliminaries regarding data models, task settings, and learning paradigms that are commonly used in related research. A hierarchical fine-grained taxonomy is further introduced to categorize existing methods in terms of their data models, learning paradigms, and techniques. From a generic perspective, we propose a unified encoder-decoder framework to formulate all the methods reviewed, where different approaches only differ in terms of some components of the framework. Moreover, we envision serving the community with an open-source project OpenTLP that refactors or implements some representative TLP methods using the proposed unified framework and summarizes other public resources. As a conclusion, we finally discuss advanced topics in recent research and highlight possible future directions.

Many network applications can be formulated as NP-hard combinatorial optimization problems of community detection (CD). Due to the NP-hardness, to balance the CD quality and efficiency remains a challenge. Most existing CD methods are transductive, which are independently optimized only for the CD on a single graph. Some of these methods use advanced machine learning techniques to obtain high-quality CD results but usually have high complexity. Other approaches use fast heuristic approximation to ensure low runtime but may suffer from quality degradation. In contrast to these transductive methods, we propose an alternative inductive community detection (ICD) method across graphs of a system or scenario to alleviate the NP-hard challenge. ICD first conducts the offline training of an adversarial dual GNN on historical graphs to capture key properties of the system. The trained model is then directly generalized to new unseen graphs for online CD without additional optimization, where a better trade-off between quality and efficiency can be achieved. ICD can also capture the permutation invariant community labels in the offline training and tackle the online CD on new graphs with non-fixed number of nodes and communities. Experiments on a set of benchmarks demonstrate that ICD can achieve a significant trade-off between quality and efficiency over various baselines.

The inclusion of the $\rho-\omega$ mixing effect is essential for a precise description of the pion electromagnetic form factor in the $e^+e^- \rightarrow \pi^+\pi^-$ process, which quantifies the two-pion contribution to the anomalous magnetic moment of the muon $a_\mu$. In this paper, we analyse the momentum dependence of the $\rho-\omega$ mixing by considering loop contributions at the next-to-leading order in the $1/N_C$ expansion within the framework of resonance chiral theory. We revisit the work [Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69 (2018) 1], considering the contribution arising from the kaon mass splitting in the kaon loops and the latest experimental data. We perform two kinds of fits (with momentum-independent or momentum-dependent $\rho-\omega$ mixing amplitude) to describe the $e^+e^-\rightarrow \pi^+\pi^-$ and $\tau\rightarrow \nu_{\tau}2\pi$ data within the energy region of 600$\sim$900 MeV and the decay width of $\omega \rightarrow \pi^+\pi^-$, and compare their results. Our findings indicate that both the momentum-independent and momentum-dependent $\rho-\omega$ mixing schemes provide appropriate descriptions of the data. However, the momentum-dependent scheme exhibits greater self-consistency, considering the reasonable imaginary part of the mixing matrix element $\Pi_{\rho\omega}$ obtained. Regarding the contribution to the anomalous magnetic moment of the muon, $a_\mu^{\pi\pi}|_{[0.6,0.9]\text{GeV}}$, the results obtained from the fits considering the momentum-dependent $\rho-\omega$ mixing amplitude agree well with those obtained without incorporating the momentum dependence of the $\rho-\omega$ mixing, within the margin of errors. Furthermore, based on the fitted values of the relevant parameters, we observe that the decay width of $\omega \rightarrow \pi^+\pi^-$ is predominantly influenced by the $\rho-\omega$ mixing effect., Comment: 24 pages, 4 figures