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IceCube, a cubic-kilometer array of optical sensors built to detect atmospheric and astrophysical neutrinos between 1 GeV and 1 PeV, is deployed 1.45 km to 2.45 km below the surface of the ice sheet at the South Pole. The classification and reconstruction of events from the in-ice detectors play a central role in the analysis of data from IceCube. Reconstructing and classifying events is a challenge due to the irregular detector geometry, inhomogeneous scattering and absorption of light in the ice and, below 100 GeV, the relatively low number of signal photons produced per event. To address this challenge, it is possible to represent IceCube events as point cloud graphs and use a Graph Neural Network (GNN) as the classification and reconstruction method. The GNN is capable of distinguishing neutrino events from cosmic-ray backgrounds, classifying different neutrino event types, and reconstructing the deposited energy, direction and interaction vertex. Based on simulation, we provide a comparison in the 1 GeV-100 GeV energy range to the current state-of-the-art maximum likelihood techniques used in current IceCube analyses, including the effects of known systematic uncertainties. For neutrino event classification, the GNN increases the signal efficiency by 18% at a fixed background rate, compared to current IceCube methods. Alternatively, the GNN offers a reduction of the background (i.e. false positive) rate by over a factor 8 (to below half a percent) at a fixed signal efficiency. For the reconstruction of energy, direction, and interaction vertex, the resolution improves by an average of 13%-20% compared to current maximum likelihood techniques in the energy range of 1 GeV-30 GeV. The GNN, when run on a GPU, is capable of processing IceCube events at a rate nearly double of the median IceCube trigger rate of 2.7 kHz, which opens the possibility of using low energy neutrinos in online searches for transient events.