Artificial neurons form the core of neuromorphic computing which is emerging as an alternative for the von Neumann computing architecture. However, existing neuron architectures still lack in area efficiency, especially considering the huge size of modern neural networks requiring millions of neurons. Here, we report on a compact leaky integrate and fire (LIF) neuron circuit based on graphene memristor device. The LIF circuit exhibits various biological properties like threshold control, leaky integration and reset behavior. Circuit parameters like the synaptic resistance and membrane capacitance act as additional control parameters whereby the spike frequency of the circuit can be effectively controlled. Uniquely, the circuit exhibits biologically realistic frequencies as low as 286 Hz. The results suggest the suitability of this compact and biorealistic LIF neuron circuit towards future bioinspired computing systems