Energy efficient, low area, and biocompatible artificial neurons are key ubiquitous components of any large scale neural systems. Previous CMOS neurons suffer from scalability drawbacks. Memristor and phase-changed neurons have variability-induced instability drawbacks, and usually rely on CMOS additional circuitry. However, graphene, despite its ballistic transport, inherently analog nature, and biocompatibility has only been considered for Boolean logic implementations. We propose an ultra-compact, all graphene-based nonlinear Leaky Integrate-and-Fire spiking neuron. We validate via SPICE its basic functionality and investigate the output spikes response under stochastic noisy input spike trains with variable firing rate. Simulation results indicate neuron robustness to noisy scenarios and neuronal output firing regularity. The small area and low energy consumption can benefit the implementation of large scale neural networks, and the biologically plausible operating conditions (e.g., 2ms and 100mV spike duration and amplitude), can promote the interfacebility of graphene based artificial neurons with biological counterparts.