论文网址：[1705.08415] Supervised Community Detection with Line Graph Neural Networks (arxiv.org)

英文是纯手打的！论文原文的summarizing and paraphrasing。可能会出现难以避免的拼写错误和语法错误，若有发现欢迎评论指正！文章偏向于笔记，谨慎食用

⭐内涵大量可视化推导

目录

1. 省流版

1.1. 心得

2. 论文逐段精读

2.1. Abstract

2.2. Introduction

2.3. Problem setup

2.4. Related works

2.5. Line Graph Neural Networks

2.5.1. Graph neural networks using a family of multiscale graph operators

2.5.2. LGNN: GNN on line graphs with the non-backtraking operator

2.5.3. A loss function invariant under label permutation

2.6. Loss landscape of linear GNN optimization

2.7. Experiments

2.7.1. Stochastic block models

2.7.2. Probing the computational-to-statistical threshold in 5-class SBM

2.7.3. Real datasets from SNAP

2.8. Conclusion

3. 知识补充

3.1. Belief propagation

4. Reference List

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1. 省流版

1.1. 心得

（1）改论文发表时间较早，许多公式表达没有统一现在的GNN，此文章统一将矩阵表示为大写字母

（2）不过这个有向信息流捕获感觉还有待商榷，还是感觉偏伪信息

2. 论文逐段精读

2.1. Abstract

        ①They proposed a family of Graph Neural Networks (GNNs)

        ②Tasks: supervised community detection

        ③GNN augmentation: non-backtracking operator on the line graph of edge adjacencies

2.2. Introduction

        LGNN can capture directed information flow from undirected graphs

2.3. Problem setup

        ①Task: node classification

        ②Graph: 

        ③Label of nodes: , where  denotes the number of communities

        ④Training set: 

        ⑤The minimized loss function:  where the predicted label is ,  is a loss function, and  represents the model

2.4. Related works