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Ejection fraction (EF) is a key indicator of cardiac function, allowing identification of patients prone to heart dysfunctions such as heart failure. EF is estimated from cardiac ultrasound videos known as echocardiograms (echo) by manually tracing the left ventricle and estimating its volume on certain frames. These estimations exhibit high inter-observer variability due to the manual process and varying video quality. Such sources of inaccuracy and the need for rapid assessment necessitate reliable and explainable machine learning techniques. In this work, we introduce EchoGNN, a model based on graph neural networks (GNNs) to estimate EF from echo videos. Our model first infers a latent echo-graph from the frames of one or multiple echo cine series. It then estimates weights over nodes and edges of this graph, indicating the importance of individual frames that aid EF estimation. A GNN regressor uses this weighted graph to predict EF. We show, qualitatively and quantitatively, that the learned graph weights provide explainability through identification of critical frames for EF estimation, which can be used to determine when human intervention is required. On EchoNet-Dynamic public EF dataset, EchoGNN achieves EF prediction performance that is on par with state of the art and provides explainability, which is crucial given the high inter-observer variability inherent in this task.