Link prediction is a key aspect of graph machine learning, with applications
as diverse as disease prediction, social network recommendations, and drug
discovery. It involves predicting new links that may form between network
nodes. Despite the clear importance of link prediction, existing models have
significant shortcomings. Graph Convolutional Networks, for instance, have been
proven to be highly efficient for link prediction on a variety of datasets.
However, they encounter severe limitations when applied to short-path networks
and ego networks, resulting in poor performance. This presents a critical
problem space that this work aims to address. In this paper, we present the
Node Centrality and Similarity Based Parameterised Model (NCSM), a novel method
for link prediction tasks. NCSM uniquely integrates node centrality and
similarity measures as edge features in a customised Graph Neural Network (GNN)
layer, effectively leveraging the topological information of large networks.
This model represents the first parameterised GNN-based link prediction model
that considers topological information. The proposed model was evaluated on
five benchmark graph datasets, each comprising thousands of nodes and edges.
Experimental results highlight NCSM's superiority over existing
state-of-the-art models like Graph Convolutional Networks and Variational Graph
Autoencoder, as it outperforms them across various metrics and datasets. This
exceptional performance can be attributed to NCSM's innovative integration of
node centrality, similarity measures, and its efficient use of topological
information.

本文提出了一种新的方法 Node Centrality and Similarity Based Parameterised Model（NCSM）用于链接预测任务，通过在自定义的图神经网络（GNN）层中将节点中心性和相似性度量作为边特征进行唯一的集成，有效地利用大型网络的拓扑信息。该模型是第一个考虑拓扑信息的参数化 GNN 链接预测模型，并在五个基准图数据集上进行评估，结果表明 NCSM 相比于现有的最先进模型如图卷积网络和变分图自编码器，在各种指标和数据集上表现出更好的性能，这种卓越的性能归功于 NCSM 对节点中心性、相似性度量的创新整合和对拓扑信息的高效利用。

基于节点中心性和图嵌入的链接预测参数化模型

A parameterised model for link prediction using node centrality and  similarity measure based on graph embedding

Graph contrastive learning (GCL) has attracted a surge of attention due to
its superior performance for learning node/graph representations without
labels. However, in practice, unlabeled nodes for the given graph usually
follow an implicit imbalanced class distribution, where the majority of nodes
belong to a small fraction of classes (a.k.a., head class) and the rest classes
occupy only a few samples (a.k.a., tail classes). This highly imbalanced class
distribution inevitably deteriorates the quality of learned node
representations in GCL. Indeed, we empirically find that most state-of-the-art
GCL methods exhibit poor performance on imbalanced node classification.
Motivated by this observation, we propose a principled GCL framework on
Imbalanced node classification (ImGCL), which automatically and adaptively
balances the representation learned from GCL without knowing the labels. Our
main inspiration is drawn from the recent progressively balanced sampling (PBS)
method in the computer vision domain. We first introduce online clustering
based PBS, which balances the training sets based on pseudo-labels obtained
from learned representations. We then develop the node centrality based PBS
method to better preserve the intrinsic structure of graphs, which highlight
the important nodes of the given graph. Besides, we theoretically consolidate
our method by proving that the classifier learned by balanced sampling without
labels on an imbalanced dataset can converge to the optimal balanced classifier
with a linear rate. Extensive experiments on multiple imbalanced graph datasets
and imbalance settings verify the effectiveness of our proposed framework,
which significantly improves the performance of the recent state-of-the-art GCL
methods. Further experimental ablations and analysis show that the ImGCL
framework remarkably improves the representations of nodes in tail classes.

本文提出了一种基于进步性平衡抽样（PBS）的图对比学习框架（ImGCL），该框架可以平衡无标签图数据的节点表示，并且在多个不平衡图数据集和不平衡设置上证明了其有效性。

ImGCL：针对不平衡节点分类的图对比学习重新审视

ImGCL: Revisiting Graph Contrastive Learning on Imbalanced Node Classification

Core-periphery detection is a key task in exploratory network analysis where
one aims to find a core, a set of nodes well-connected internally and with the
periphery, and a periphery, a set of nodes connected only (or mostly) with the
core. In this work we propose a model of core-periphery for higher-order
networks modeled as hypergraphs and we propose a method for computing a
core-score vector that quantifies how close each node is to the core. In
particular, we show that this method solves the corresponding non-convex
core-periphery optimization problem globally to an arbitrary precision. This
method turns out to coincide with the computation of the Perron eigenvector of
a nonlinear hypergraph operator, suitably defined in term of the incidence
matrix of the hypergraph, generalizing recently proposed centrality models for
hypergraphs. We perform several experiments on synthetic and real-world
hypergraphs showing that the proposed method outperforms alternative
core-periphery detection algorithms, in particular those obtained by
transferring established graph methods to the hypergraph setting via clique
expansion.

本文提出了一种基于超图的核心 - 边缘模型，通过对高阶网络的核心分数向量进行计算，解决了对应的非凸核心 - 边缘优化问题，被证明在人工合成和真实世界的网络数据集中表现得比竞争算法要好。

超图中的核心 - 边缘检测

Core-periphery detection in hypergraphs

Graph embedding provides an efficient solution for graph analysis by
converting the graph into a low-dimensional space which preserves the structure
information. In contrast to the graph structure data, the i.i.d. node embedding
can be processed efficiently in terms of both time and space. Current
semi-supervised graph embedding algorithms assume the labelled nodes are given,
which may not be always true in the real world. While manually label all
training data is inapplicable, how to select the subset of training data to
label so as to maximize the graph analysis task performance is of great
importance. This motivates our proposed active graph embedding (AGE) framework,
in which we design a general active learning query strategy for any
semi-supervised graph embedding algorithm. AGE selects the most informative
nodes as the training labelled nodes based on the graphical information (i.e.,
node centrality) as well as the learnt node embedding (i.e., node
classification uncertainty and node embedding representativeness). Different
query criteria are combined with the time-sensitive parameters which shift the
focus from graph based query criteria to embedding based criteria as the
learning progresses. Experiments have been conducted on three public data sets
and the results verified the effectiveness of each component of our query
strategy and the power of combining them using time-sensitive parameters. Our
code is available online at: this https URL

本论文提出了一个称为主动图嵌入（AGE）的框架，用于选择最具信息量的节点作为训练有标签节点，以提高半监督图嵌入算法的性能，并结合具有时间敏感性的参数。实验结果表明我们所提出的查询策略的每个组成部分的有效性以及使用时间敏感性参数进行组合的强大性。