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In image generation, generative models can be evaluated naturally by visually inspecting model outputs. However, this is not always the case for graph generative models (GGMs), making their evaluation challenging. Currently, the standard process for evaluating GGMs suffers from three critical limitations: i) it does not produce a single score which makes model selection challenging, ii) in many cases it fails to consider underlying edge and node features, and iii) it is prohibitively slow to perform. In this work, we mitigate these issues by searching for scalar, domain-agnostic, and scalable metrics for evaluating and ranking GGMs. To this end, we study existing GGM metrics and neural-network-based metrics emerging from generative models of images that use embeddings extracted from a task-specific network. Motivated by the power of certain Graph Neural Networks (GNNs) to extract meaningful graph representations without any training, we introduce several metrics based on the features extracted by an untrained random GNN. We design experiments to thoroughly test metrics on their ability to measure the diversity and fidelity of generated graphs, as well as their sample and computational efficiency. Depending on the quantity of samples, we recommend one of two random-GNN-based metrics that we show to be more expressive than pre-existing metrics. While we focus on applying these metrics to GGM evaluation, in practice this enables the ability to easily compute the dissimilarity between any two sets of graphs regardless of domain. Our code is released at: https://github.com/uoguelph-mlrg/GGM-metrics.