In this paper, we propose a novel pooling layer for graph neural networks based on maximizing the mutual information between the pooled graph and the input graph. Since the maximum mutual information is difficult to compute, we em- ploy the Shannon capacity of a graph as an inductive bias to our pooling method. More precisely, we show that the input graph to the pooling layer can be viewed as a representation of a noisy communication channel. For such a channel, send- ing the symbols belonging to an independent set of the graph yields a reliable and error-free transmission of information. We show that reaching the maximum mutual information is equivalent to finding a maximum weight independent set of the graph where the weights convey entropy contents. Through this communica- tion theoretic standpoint, we provide a distinct perspective for posing the problem of graph pooling as maximizing the information transmission rate across a noisy communication channel, implemented by a graph neural network. We evaluate our method, referred to as Maximum Entropy Weighted Independent Set Pooling (MEWISPool), on graph classification tasks and the combinatorial optimization problem of the maximum independent set. Empirical results demonstrate that our method achieves the state-of-the-art and competitive results on graph classification tasks and the maximum independent set problem in several benchmark datasets.

• Python >= 3.6.
• Pytorch=1.9.0.
• Torch Geometric=1.5.0

For running the graph classification code, initially clone the repository. Give the execution permission to run_graph_classification.sh: chmod +x run_graph_classification.sh. Finally, run ./run_graph_classification.sh. For the MIS task, follow the same procedure for the run_mis.sh. Note that the graph classification experiment is conducted over the MUTAG dataset and the MIS task is solved over the Cora dataset.

In case of failure in installation of the dependencies, please refer to Pytorch Installation and Torch Geometric Installation.