Graph convolutional networks are becoming indispensable for deep learning
from graph-structured data. Most of the existing graph convolutional networks
share two big shortcomings. First, they are essentially low-pass filters, thus
the potentially useful middle and high frequency band of graph signals are
ignored. Second, the bandwidth of existing graph convolutional filters is
fixed. Parameters of a graph convolutional filter only transform the graph
inputs without changing the curvature of a graph convolutional filter function.
In reality, we are uncertain about whether we should retain or cut off the
frequency at a certain point unless we have expert domain knowledge. In this
paper, we propose Automatic Graph Convolutional Networks (AutoGCN) to capture
the full spectrum of graph signals and automatically update the bandwidth of
graph convolutional filters. While it is based on graph spectral theory, our
AutoGCN is also localized in space and has a spatial form. Experimental results
show that AutoGCN achieves significant improvement over baseline methods which
only work as low-pass filters.

本文提出了 Automatic Graph Convolutional Networks (AutoGCN) 来捕获图信号的全部频谱，并自动更新图卷积滤波器的带宽，实验结果表明，AutoGCN 比只能作为低通滤波器的基准方法有了显著的改进。

超越低通滤波：自动过滤的图卷积网络

Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic  Filtering

We interpret the subgraph centrality as the partition function of a network.
The entropy, the internal energy and the Helmholtz free energy are defined for
networks and molecular graphs on the basis of graph spectral theory. Various
relations of these quantities to the structure and the dynamics of the complex
networks are discussed. They include the cohesiveness of the network and the
critical coupling of coupled phase oscillators. We explore several models of
network growing/evolution as well as real-world networks, such as those
representing metabolic and protein-protein interaction networks as well as the
interaction between secondary structure elements in proteins.

通过图谱理论将亚图中心性解释为网络的配分函数，定义了网络和分子图的熵、内能和亥姆霍兹自由能，并讨论了这些量与复杂网络结构和动力学的各种关系。包括网络的紧密度以及耦合相位振荡器的临界耦合。我们探讨了多个网络生长 / 演化模型以及代表代谢和蛋白质相互作用网络以及蛋白质中二级结构元素相互作用的真实世界网络。