 This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic, Kalmogorov complexity, and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined, and intrinsic, classical measures, and extrinsic, corner entropy, variants of entropy-based models are discussed in some detail. This article was authored by Matthias Demmer and Abbey Mosiewicz.