Abstract Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal constraints, such as journeys or, more generally, existential constraints, possibly with finite delays. In this paper we propose to use timed automata to express temporal constraints, leading to a general and powerful notion of temporal basic graph pattern (BGP). The new difficulty is the evaluation of the temporal constraint on a large set of matchings. An important benefit of timed automata is that they support an iterative state assignment, which can be useful for early detection of matches and pruning of non-matches. We introduce algorithms to retrieve all instances of a temporal BGP match in a graph, and present results of an extensive experimental evaluation, demonstrating interesting performance trade-offs. We show that an on-demand algorithm that processes total matchings incrementally over time is preferable when dealing with cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and when connectivity of partial matchings can be guaranteed, the best performance is achieved by maintaining partial matchings over time and allowing automaton evaluation to be fully incremental. The code and datasets used in our analysis are available at http://github.com/amirpouya/TABGP .

In the last decade, substantial progress has been made towards standardizing the syntax of graph query languages, and towards understanding their semantics and complexity of evaluation. In this paper, we consider temporal property graphs (TPGs) and propose temporal regular path queries (TRPQs) that incorporate time into TPG navigation. Starting with design principles, we propose a natural syntactic extension of the MATCH clause of popular graph query languages. We then formally present the semantics of TRPQs, and study the complexity of their evaluation. We show that TRPQs can be evaluated in polynomial time if TPGs are time-stamped with time points, and identify fragments of the TRPQ language that admit efficient evaluation over a more succinct interval-annotated representation. Finally, we implement a fragment of the language in a state-of-the-art dataflow framework, and experimentally demonstrate that TRPQ can be evaluated efficiently.