Graph self-supervised learning aims to learn the intrinsic graph representations from unlabeled data, with broad applicability in areas such as computing networks. Although graph contrastive learning (GCL) has achieved remarkable progress by generating perturbed views via data augmentation and optimizing sample similarity, it performs poorly in heterophilic graph scenarios (where connected nodes are likely to belong to different classes or exhibit dissimilar features). In heterophilic graphs, existing methods typically rely on random or carefully designed augmentation strategies (e.g., edge dropping) for contrastive views. However, such graph structures exhibit intricate edge relationships, where topological perturbations may completely alter the semantics of neighborhoods. Moreover, most methods focus solely on local contrastive signals while neglecting global structural constraints. To address these limitations, inspired by graph coloring, we propose a novel Coloring learning for heterophilic graph Representation framework, CoRep, which: 1) Pioneers a coloring classifier to generate coloring labels, explicitly minimizing the discrepancy between homophilic nodes while maximizing that of heterophilic nodes. A global positive sample set is constructed using multi-hop same-color nodes to capture global semantic consistency.

Temporal graph link prediction aims to predict future interactions between nodes in a graph based on their historical interactions, which are encoded in node embeddings. We observe that heterogeneity naturally appears in temporal interactions, e.g., a few node pairs can make most interaction events, and interaction events happen at varying intervals. This leads to the problems of ineffective temporal information encoding and forgetting of past interactions for a pair of nodes that interact intermittently for their link prediction. Existing methods, however, do not consider such heterogeneity in their learning process, and thus their learned temporal node embeddings are less effective, especially when predicting the links for infrequently interacting node pairs. To cope with the heterogeneity, we propose a novel framework called TAMI, which contains two effective components, namely log time encoding function (LTE) and link history aggregation (LHA). LTE better encodes the temporal information through transforming interaction intervals into more balanced ones, and LHA prevents the historical interactions for each target node pair from being forgotten. State-of-the-art temporal graph neural networks can be seamlessly and readily integrated into TAMI to improve their effectiveness. Experiment results on 13 classic datasets and three newest temporal graph benchmark (TGB) datasets show that TAMI consistently improves the link prediction performance of the underlying models in both transductive and inductive settings.

Temporal graph link prediction aims to predict future interactions between nodes in a graph based on their historical interactions, which are encoded in node embeddings. We observe that heterogeneity naturally appears in temporal interactions, e.g., a few node pairs can make most interaction events, and interaction events happen at varying intervals. This leads to the problems of ineffective temporal information encoding and forgetting of past interactions for a pair of nodes that interact intermittently for their link prediction. Existing methods, however, do not consider such heterogeneity in their learning process, and thus their learned temporal node embeddings are less effective, especially when predicting the links for infrequently interacting node pairs. To cope with the heterogeneity, we propose a novel framework called TAMI, which contains two effective components, namely log time encoding function (LTE) and link history aggregation (LHA). LTE better encodes the temporal information through transforming interaction intervals into more balanced ones, and LHA prevents the historical interactions for each target node pair from being forgotten. State-of-the-art temporal graph neural networks can be seamlessly and readily integrated into TAMI to improve their effectiveness. Experiment results on 13 classic datasets and three newest temporal graph benchmark (TGB) datasets show that TAMI consistently improves the link prediction performance of the underlying models in both transductive and inductive settings. Our code is available at https://github.com/Alleinx/TAMI

Network embedding plays a significant role in a variety of applications. To capture the topology of the network, most of the existing network embedding algorithms follow a sampling training procedure, which maximizes the similarity (e.g., embedding vectors' dot product) between positively sampled node pairs and minimizes the similarity between negatively sampled node pairs in the embedding space. Typically, close node pairs function as positive samples while distant node pairs are usually considered as negative samples. However, under different or even competing sampling strategies, some methods champion sampling distant node pairs as positive samples to encapsulate longer distance information in link prediction, whereas others advocate adding close nodes into the negative sample set to boost the performance of node recommendation. In this paper, we seek to understand the intrinsic relationships between these competing strategies. To this end, we identify two properties (discrimination and monotonicity) that given any node pair proximity distribution, node embeddings should embrace. Moreover, we quantify the empirical error of the trained similarity score w.r.t. the sampling strategy, which leads to an important finding that the discrimination property and the monotonicity property for all node pairs can not be satisfied simultaneously in real-world applications. Guided by such analysis, a simple yet novel model (SENSEI) is proposed, which seamlessly fulfills the discrimination property and the partial monotonicity within the top-K ranking list. Extensive experiments show that SENSEI outperforms the state-of-the-arts in plain network embedding.

Link prediction, which aims to forecast unseen connections in graphs, is a fundamental task in graph machine learning. Heuristic methods, leveraging a range of different pairwise measures such as common neighbors and shortest paths, often rival the performance of vanilla Graph Neural Networks (GNNs). Therefore, recent advancements in GNNs for link prediction (GNN4LP) have primarily focused on integrating one or a few types of pairwise information. In this work, we reveal that different node pairs within the same dataset necessitate varied pairwise information for accurate prediction and models that only apply the same pairwise information uniformly could achieve suboptimal performance.As a result, we propose a simple mixture of experts model Link-MoE for link prediction. Link-MoE utilizes various GNNs as experts and strategically selects the appropriate expert for each node pair based on various types of pairwise information. Experimental results across diverse real-world datasets demonstrate substantial performance improvement from Link-MoE. Notably, Link-Mo achieves a relative improvement of 18.71% on the MRR metric for the Pubmed dataset and 9.59% on the Hits@100 metric for the ogbl-ppa dataset, compared to the best baselines. The code is available at https://github.com/ml-ml/Link-MoE/.

Based on our definitions, we identify and analyze six real-world benchmarks spanning from homophilic to heterophilic link prediction settings, with graphs containing up to 30M edges.

In this work, wepresent G2SAT,thefirst deep generativeframework that learns to generate SAT formulas from a given set of input formulas.

A.1 CommunityDetection The spectral clustering algorithm for directed networks that we consider in this paper is shown in Algorithm A.1. It can be applied either to the weighted adjacency (count) matrixN or the unweighted adjacency matrixA, where Aij =1{Nij >0} and 1{ } denotes the indicator function of the argument. This algorithm is used for the community detection step in our proposed CHIP estimationprocedure. For undirectednetworks, which we use for the theoreticalanalysisin Section 4, spectral clustering is performed by running k-means clustering on the rows of theeigenvector matrix of N or A, not the rows of the concatenated singular vector matrix. A.2 Estimation of Hawkes process parameters Ozaki (1979) derived the log-likelihood function for Hawkes processes with exponential kernels, which takes the form: logL= µT+ The threeparameters µ,α,β can be estimatedby maximizing (A.1) using standard numerical methods for non-linear optimization (Nocedal & Wright, 2006). We provide closed-form equations for estimating mab =αab/βab and µab in (2).