Graphs are ubiquitous and ever-present data structures that have a wide range of applications involving social networks, knowledge bases and biological interactions. The evolution of a graph in such scenarios can yield important insights about the nature and ac- tivities of the underlying network, which can then be utilized for applications such as news dissemination, network monitoring, and content curation. Capturing the continuous evolution of a graph can be achieved by long-standing sub-graph queries. Although, for many applications this can only be achieved by a set of quer- ies, state-of-the-art approaches focus on a single query scenario. In this paper, we therefore introduce the notion of continuous multi-query processing over graph streams and discuss its appli- cation to a number of use cases. To this end, we designed and developed a novel algorithmic solution for efficient multi-query evaluation against a stream of graph updates and experimentally demonstrated its applicability. Our results against two baseline approaches using real-world, as well as synthetic datasets, confirm a two orders of magnitude improvement of the proposed solution.