An Introduction to Temporal Graphs: An Algorithmic Perspective^*

Abstract

A temporal graph is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed as a sequence G1, G2 . . . , G l of static graphs over the same (static) set of nodes V . Though static graphs have been extensively studied, for their temporal generalization we are still far from having a concrete set of structural and algorithmic principles. Recent research shows that many graph properties and problems become radically different and usually substantially more difficult when an extra time dimension in added to them. Moreover, there is already a rich and rapidly growing set of modern systems and applications that can be naturally modeled and studied via temporal graphs. This, further motivates the need for the development of a temporal extension of graph theory. We survey here recent results on temporal graphs and temporal graph problems that have appeared in the Computer Science community. Supported in part by the project "Foundations of Dynamic Distributed Computing Systems" (FOCUS) which is implemented under the "ARISTEIA" Action of the Operational Programme "Education and Lifelong Learning" and is co-funded by the European Union

Event Graphs: Advances and Applications of Second-Order Time-Unfolded Temporal Network Models

“…One way to preserve the temporal ordering of paths is by considering time-unfolded (or time-node) graph [32,45]. Here nodes are replaced by time-indexed copies of themselves and edges can only travel from older to newer timeindexed nodes.…”

Using Compressed Suffix-Arrays for a compact representation of temporal-graphs

“…For example, given Figure 2 Note that all previous queries have a time-instant or a time-interval version. In what follows, we concentrate on time-instant queries, which can be easily extended to answer time-interval queries, and they also serve as the building blocks for more complex temporal measures that are based on recovering time-respecting paths [32].…”

“…Notice that the vertexes b and c are only reachable from the vertex a because the edges reaching d are not available. Therefore, taking into account the temporal dynamism of graphs allows us to exploit information about temporal correlations and causality, which would be unfeasible through a classical analysis of static graphs [36,19,32]. A direct approach to represent temporal graphs could be a time-ordered sequence of snapshots ( Figure 1a), one for each time instant, showing the state of the temporal graph at a time instant as a static graph.…”

Graph Stories in Small Area

“…Further related results appear in [6,10,11,15,17,19]; in particular, geometric simultaneous embeddings [4,5] are closely related to the setting we consider in this paper. Contributions focused on the information-visualization aspects of dynamic graphs are surveyed in [2]; further, a survey on temporal graph problems appears in [16].…”