Temporal graph algebra

Graph representations underlie many modern computer applications, capturing the structure of such diverse networks as the Internet, personal associations, roads, sensors, and metabolic pathways. While analysis of static graphs is a well-explored field, new emphasis is being placed on understanding and representing the ways in which networks change over time. Current research is delving into graph evolution rate and mechanisms, the impact of specific events on network evolution, and spatial and spatio-temporal patterns. However, systematic support for evolving graph querying and analytics still lacks. Our goal is to fill this gap, giving users an ability to concisely express a wide range of common analysis tasks. In this paper we combine advances in graph databases and in temporal relational databases and propose an evolving graph model, including a representation called TGraph and an algebra called TGA, that adheres to point-based semantics. TGA includes principled temporal generalizations of conventional graph operators, as well as novel operators that support exploratory analysis of evolving graphs at different levels of temporal and structural granularity.