Neural networks require both a weighting of inputs and a nonlinear activation function operating on their sum. Neural network weighting has been demonstrated in integrated photonics with both interferometric and ring-based wavelength division multiplexing. While direct nonlinearity in optics is difficult to achieve without high optical powers, an electro-optic nonlinearity can be created by directly coupling a photodiode to electro-optic modulator. The low capacitance of directly coupling the components results in operating speeds >10 GHz with relatively low power consumption. Here we present a closed form equation for the activation functions created by graphene and quantum well electro-optic absorption modulators capacitively coupled to photodiodes. Our modulator-geometry based and thermal-noise analysis shows that such electro-optic neurons produce SNRs around 60. Performing an MNIST classification inference test on a feed-forward neural network with these electrooptic nodes, with accuracies of about 95% starting a laser power level around 5mW and 20mW for the QW and Graphene-based modulator, respectively. Our findings show regions of realistic operating performance of future optical and photonic neural networks using electro-optic analogue (non-spiking)neurons.