This paper concerns the structure of phonological neighbourhood networks, which are a graph-theoretic representation of the phonological lexicon. These networks represent each word as a node and links are placed between words which are phonological neighbours, usually defined as a string edit distance of one. Phonological neighbourhood networks have been used to study many aspects of the mental lexicon and psycholinguistic theories of speech production and perception. This paper offers preliminary graph-theoretic observations about phonological neighbourhood networks considered as a class. To aid this exploration, this paper introduces the concept of the hyperlexicon, the network consisting of all possible words for a given symbol set and their neighbourhood relations. The construction of the hyperlexicon is discussed, and basic properties are derived. This work is among the first to directly address the nature of phonological neighbourhood networks from an analytic perspective.