Graph-Theoretic Analysis of de Bruijn Graphs: Fault Resilience and Fragility

The de Bruijn graph, initially proposed as a topological architecture for interconnection networks, offers unique attributes. These graphs are regular, Eulerian, and Hamiltonian, boasting a small diameter close to optimal connectivity. Their low average distance, small diameter, and high connectivity contribute to remarkable fault tolerance against both node and edge failures. Comprehensively, these graphs serve as pivotal components in word-representing networks, finding applications in various scientific and engineering domains, particularly in genome assembly. They play a significant role in bioinformatics, information theory, coding, communication networks, and multiprocessors. Additionally, de Bruijn graphs are utilized in peer-to-peer (P۲P) networks and distributed hash tables (DHT), demonstrating their versatility. Moreover, de Bruijn graphs can serve as a robust infrastructure for modeling online/offline user behavior. In this article, we delve into the different types of de Bruijn graphs and their unique properties from a graph theory perspective. Our focus is on evaluating the reliability of these graphs concerning resilience, fragility, and vulnerability to random failures and targeted attacks on both nodes and edges.

Keywords:

Graph theory , Interconnection Networks , de Bruijn Graph , Fault-Tolerance , Graph Resilience , Network Fragility