Archaeological excavations in the sites of the Indus Valley civilization (2500–1900 BCE) in Pakistan and northwestern India have unearthed a large number of artifacts with inscriptions made up of hundreds of distinct signs. To date, there is no generally accepted decipherment of these sign sequences, and there have been suggestions that the signs could be non-linguistic. Here we apply complex network analysis techniques to a database of available Indus inscriptions, with the aim of detecting patterns indicative of syntactic organization. Our results show the presence of patterns, e.g., recursive structures in the segmentation trees of the sequences, that suggest the existence of a grammar underlying these inscriptions.