In this paper, we propose a novel pooling layer for graph neural networks\nbased on maximizing the mutual information between the pooled graph and the\ninput graph. Since the maximum mutual information is difficult to compute, we\nemploy the Shannon capacity of a graph as an inductive bias to our pooling\nmethod. More precisely, we show that the input graph to the pooling layer can\nbe viewed as a representation of a noisy communication channel. For such a\nchannel, sending the symbols belonging to an independent set of the graph\nyields a reliable and error-free transmission of information. We show that\nreaching the maximum mutual information is equivalent to finding a maximum\nweight independent set of the graph where the weights convey entropy contents.\nThrough this communication theoretic standpoint, we provide a distinct\nperspective for posing the problem of graph pooling as maximizing the\ninformation transmission rate across a noisy communication channel, implemented\nby a graph neural network. We evaluate our method, referred to as Maximum\nEntropy Weighted Independent Set Pooling (MEWISPool), on graph classification\ntasks and the combinatorial optimization problem of the maximum independent\nset. Empirical results demonstrate that our method achieves the\nstate-of-the-art and competitive results on graph classification tasks and the\nmaximum independent set problem in several benchmark datasets.\n