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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 athttp://github.com/amirpouya/TABGP. 

In recent years there has been significant interest in evolutionary analysis of large-scale networks. Researchers study network evolution rate and mechanisms, the impact of specific events on evolution, and spatial and spatio-temporal patterns. To support data scientists who are studying network evolution, there is a need to develop scalable and generalizable systems. Tangible systems progress in turn depends on the availability of standardized datasets on which performance can be tested. In this work, we make progress towards a data generator for evolving property graphs, which represent evolution of graph topology, and of vertex and edge attributes. We propose an attribute-based model of preferential attachment, and instantiate this model on a co-authorship network derived from DBLP, with attributes representing publication venues of the authors. We show that this attribute-based model predicts which edges are created more accurately than a structure-only model. Finally, we demonstrate that synthetic graphs are indeed useful for evaluating performance of evolving graph query primitives.