The property graph data model of modern graph database systems is increasingly adapted for storing and processing heterogeneous datasets like networks. Many challenging applications with near real-time requirements -- e.g. financial fraud detection, recommendation systems, and on-the-fly validation -- can be captured with graph queries, which are evaluated repeatedly. To ensure quick response time for a changing data set, these applications would benefit from applying incremental view maintenance (IVM) techniques, which can perform continuous evaluation of queries and calculate the changes in the result set upon updates. However, currently, no graph databases provide support for incremental views. While IVM problems have been studied extensively over relational databases, views on property graph queries require operators outside the scope of standard relational algebra. Hence, tackling this problem requires the integration of numerous existing IVM techniques and possibly further extensions. In this paper, we present an approach to perform IVM on property graphs, using a nested relational algebraic representation for property graphs and graph operations. Then we define a chain of transformations to reduce most property graph queries to flat relational algebra and use techniques from discrimination networks (used in rule-based expert systems) to evaluate them. We demonstrate the approach using our prototype tool, ingraph, which uses openCypher, an open graph query language specified as part of an industry initiative. However, several aspects of our approach can be generalised to other graph query languages such as G-CORE and PGQL.