Temporal Graph Traversals: Definitions, Algorithms, and Applications

TL;DR

This paper introduces new definitions and efficient algorithms for depth-first and breadth-first search in temporal graphs, addressing unique challenges posed by time-dependent connections and demonstrating their practical effectiveness.

Contribution

It proposes novel definitions and algorithms for temporal graph traversals, filling a gap in understanding and processing time-aware graph data.

Findings

Proposed efficient algorithms with optimal complexity

Validated algorithms on real-world temporal graphs

Enhanced understanding of temporal traversal properties

Abstract

A temporal graph is a graph in which connections between vertices are active at specific times, and such temporal information leads to completely new patterns and knowledge that are not present in a non-temporal graph. In this paper, we study traversal problems in a temporal graph. Graph traversals, such as DFS and BFS, are basic operations for processing and studying a graph. While both DFS and BFS are well-known simple concepts, it is non-trivial to adopt the same notions from a non-temporal graph to a temporal graph. We analyze the difficulties of defining temporal graph traversals and propose new definitions of DFS and BFS for a temporal graph. We investigate the properties of temporal DFS and BFS, and propose efficient algorithms with optimal complexity. In particular, we also study important applications of temporal DFS and BFS. We verify the efficiency and importance of our graph traversal algorithms in real world temporal graphs.