Graph Connectivity and Fault Tolerance in Network Systems
Summary
Graph connectivity and fault tolerance form the theoretical backbone of resilient network design. Connectivity measures the minimal number of elements—nodes or links—whose removal disrupts communication among remaining components. Higher connectivity implies greater inherent robustness against random failures or targeted attacks. Fault tolerance complements connectivity by quantifying the ability of a network to continue functioning under various fault models, including node removals, link degradations or clustered failures. Over recent years, researchers have developed refined metrics, such as ℓ-component connectivity, structure connectivity and substructure connectivity, to capture nuanced failure modes beyond classical vertex- or edge-connectivity. These metrics have been applied to a spectrum of interconnection topologies—hypercubes, toroidal meshes, k-ary n-cubes and Cayley-graph-based networks—revealing trade-offs between scalability, diameter, routing complexity and fault resilience. Practical applications span high-performance computing, distributed sensor grids, on-chip networks and large-scale data centres. The interplay between theoretical bounds and algorithmic constructions, such as independent spanning trees and fault-tolerant routing schemes, underpins continual advances in ensuring uninterrupted service in critical infrastructures worldwide.
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Graph Connectivity and Fault Tolerance in Network Systems publication trend
The graph below shows the total number of articles in graph connectivity and fault tolerance in network systems across all publications each year (not limited to Nature Index journals).
Technical terms
Vertex connectivity: The minimum number of vertices whose removal disconnects a graph.
Edge connectivity: The minimum number of edges whose removal disconnects a graph.
ℓ-component connectivity: The smallest set of vertices whose removal yields at least ℓ disconnected components or reduces the graph below ℓ nodes.
Structure connectivity: The minimum number of subgraphs, each isomorphic to a given template, whose removal disconnects the host graph.
Substructure connectivity: The minimum number of subgraphs, each isomorphic to any connected subgraph of a template, whose removal disconnects the host graph.
Fault tolerance: The capacity of a network to sustain correct operation despite failures of its components.
References
- Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity. IEEE Access (2019).
- Structure Connectivity and Substructure Connectivity of $k$ -Ary $n$ -Cube Networks. IEEE Access (2019).
- Cluster-Fault Tolerant Routing in a Torus. Sensors (2020).
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