概念

G=(V,E)
V={v1,v2,v3,v4,v5,v6,v7,v8,v9,v10,v11}
E={(v1,v2),(v2,v3),(v2,v6),(v3,v7)...}
|V|=11
|E|=11

Walk: close walk x=y otherwise open walk
Trail: x - y trail is a walk with no repeated edge，没有重复走边
Path: x - y path is a walk with no repeated Vertex,没有走重复的点
Cycle: x - x path is a cycle
Circuit: x - x trail is a circuit
Degree:点有多少个边连出去，度

Regular graph：每个点有相同的度
Complete graph:图像任意两个点都有边
Simple graph:一个图没有self-loop的点
Multigraph: A graph with multiple edges
Pseudograph:有self-loop也有multiple edges

Hypergraph: Allow an edge connected to multiple vertcies

三类任务：

1 节点层面任务：比如文章最开始提到的引文网络中，节点论文的分类，社交网络中用户标签的分类等。此时，主要关注节点和边层面的特征。
2 边层面任务：比如社交网络中，将用户作为节点，用户之间的关注关系建模为边，通过边预测实现社交用户的推荐。此时，主要关注节点和边的特征。
3 图层面的任务：比如对药物分子的分类。此时，任务不依赖于某个节点或某条边的属性，而是，需要考虑整个图的信息。

图嵌入、图神经网络、图卷积的关系:

查看图神经网络的资料，最常见图嵌入（Graph Embedding）、图神经网络（GNN）、图卷积（GCN）这三个词，同时，也很容易迷惑：到底这三个说的是三个东西还是一个东西？大家平时说的图网络指的是哪一个？这三个有什么联系？图神经网络是一个很宽泛的概念，图神经网络=图+神经网络。我们通俗讲的图神经网络主要指GNN和GCN（类似于深度学习网络中的前馈全连接DNN和CNN）。

图嵌入发展较早，在早期是一个相对独立的领域，关注的问题大致分为4类：

1、节点分类
2、链接预测
3、聚类
4、可视化

方法主要分为三类：

基于因子分解的方法
基于随机游走的方法
基于深度学习的方法

GNN的分类：

Graph convolution networks
Graph attention networks
Graph autoencoders
Graph generative networks
Graph spatial-temporal networks

GCN分类：

Spectral-based GCN————基于频谱域的GCN
Spatial-based GCN————基于空域的GCN

x是feature
把A做特征分解

先拉普拉斯在做特征分解
傅里叶变换
ChebNet MPNN

节点并缩

GAT (Graph attention networks)

attention：key和一个query 比较和哪些key相似，得到一个weight
拿中间的点当query---i 和周围的key---j比较
比较像的话α就比较大

transformer --- Multi-head attention

Graph autoencoder(GAE)

Variational graph autoencoder(VGAE)

CVPR/KDD/ECCV/ICML2020的关于图卷积网络的论文：

[CVPR 2020] Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud
[CVPR 2020] Geometrically Principled Connections in Graph Neural Networks [CVPR 2020] SuperGlue: Learning Feature Matching With Graph Neural Networks
[CVPR 2020] Learning Multi-View Camera Relocalization With Graph Neural Networks
[CVPR 2020] Multi-Modal Graph Neural Network for Joint Reasoning on Vision and Scene Text
[CVPR 2020] Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory
[CVPR 2020] Dynamic Multiscale Graph Neural Networks for 3D Skeleton Based Human Motion Prediction
[CVPR 2020] Dynamic Graph Message Passing Networks
[ECCV 2020] Graph convolutional networks for learning with few clean and many noisy labels
[ICML 2020] When Spectral Domain Meets Spatial Domain in Graph Neural Networks
[KDD 2020] Graph Structural-topic Neural Network
[KDD 2020] Towards Deeper Graph Neural Networks
[KDD 2020] Redundancy-Free Computation for Graph Neural Networks
[KDD 2020] TinyGNN: Learning Efficient Graph Neural Networks
[KDD 2020] PolicyGNN: Aggregation Optimization for Graph Neural Networks [KDD 2020] Residual Correlation in Graph Neural Network Regression
[KDD 2020] Spotlight: Non-IID Graph Neural Networks
[KDD 2020] XGNN: Towards Model-Level Explanations of Graph Neural Networks
[KDD 2020] Dynamic Heterogeneous Graph Neural Network for Real-time Event Prediction
[KDD 2020] Handling Information Loss of Graph Neural Networks for Session-based Recommendation
[KDD 2020] Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks
[KDD 2020] GPT-GNN: Generative Pre-Training of Graph Neural Networks
[KDD 2020] Graph Structure Learning for Robust Graph Neural Networks
[KDD 2020] Minimal Variance Sampling with Provable Guarantees for Fast Training of Graph Neural Networks
[KDD 2020] A Framework for Recommending Accurate and Diverse Items Using Bayesian Graph Convolutional Neural Networks
[KDD 2020] Competitive Analysis for Points of Interest
[KDD 2020] Knowing your FATE: Explanations for User Engagement Prediction on Social Apps
[KDD 2020] GHashing: Semantic Graph Hashing for Approximate Similarity Search in Graph Databases
[KDD 2020] Comprehensive Information Integration Modeling Framework for Video Titling`

相关paper

1.A Comprehensive Survey on Graph Neural Networks
2.Relational inductive biases, deep learning, and graph networks
3.Geometric deep learning: going beyond Euclidean data
4.The Graph Neural Network Model
5.Variational Graph Auto-encoders
6.Neural Message Passing for Quantum Chemistry
7.DIFFUSION CONVOLUTIONAL RECURRENT NEURAL NETWORK: DATA DRIVEN TRAFFIC FORECASTING
8.GRAPH ATTENTION NETWORKS
9.MOLGAN: An implicit generative model for small molecular graphs

论文综述目前较推荐的有这三篇：
《Graph Neural Networks: A Review of Methods and Applications》
《Deep Learning on Graphs: A Survey》
《A Comprehensive Survey on Graph Neural Networks》
机器之心对这三篇综述还有专门的报道，《图神经网络概述第三弹：来自IEEE Fellow的GNN综述》
北师大的集智学园
中科院的人工智能前沿讲习
这两个主页上有不少图网络相关的视频，视频质量也不错。

参考文献
《图嵌入（Graph embedding）综述》
《【论文笔记】DeepWalk》
《The Graph Neural Network Model》
《GNN 简介和入门资料》
《Learning Convolutional Neural Networks for Graphs》
《Learning Convolutional Neural Networks for Graphs-PPT》
《论文笔记：Learning Convolutional Neural Networks for Graphs》
《Semi-Supervised Classification with Graph Convolutional Networks》
《Semi-Supervised Classification with Graph Convolutional Networks阅读笔记》
《Abusive Language Detection with Graph Convolutional Networks》
《Spam Review Detection with Graph Convolutional Networks》
《Graph Neural Networks: A Review of Methods and Applications》
《Deep Learning on Graphs: A Survey》
《A Comprehensive Survey on Graph Neural Networks》
图神经网络概述第三弹：来自IEEE Fellow的GNN综述》
哔哩哔哩上有视频
《唐杰-图神经网络及认知推理-图神经网络学习班》
《图神经网络介绍-Introduction to GNN》