Abstract: Online conversations are particularly susceptible to derailment, which can manifest itself in the form of toxic communication patterns like disrespectful comments or verbal abuse. Forecasting conversation derailment predicts signs of derailment in advance enabling proactive moderation of conversations. Current state-of-the-art approaches to address this problem rely on sequence models that treat dialogues as text streams. We propose a novel model based on a graph convolutional neural network that considers dialogue user dynamics and the influence of public perception on conversation utterances. Through empirical evaluation, we show that our model effectively captures conversation dynamics and outperforms the state-of-the-art models on the CGA and CMV benchmark datasets by 1.5\textbackslash{}\% and 1.7\textbackslash{}\%, respectively.