Graph Theory¶
Bondy, J. A., & Murty, U. S. R. (2008). Graph Theory. Springer.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Cut
- Cut-based formulation of clustering and segmentation: finding a partition with small inter-part interaction is one problem under many disguises — community detection, image segmentation, module finding. Resilience as cut hardness: a network tolerates \(k\) failures exactly when its minimum cut exceeds \(k\), which turns a vague resilience goal into a clean quantitative target.
This sourceGraduate Texts in Mathematics 244. New York: Springer, 2008. Standard reference for connectivity: a graph is k-edge-connected iff its minimum edge cut is at least k, so a network tolerates k−1 edge failures (resilience as cut hardness).
- Cut-based formulation of clustering and segmentation: finding a partition with small inter-part interaction is one problem under many disguises — community detection, image segmentation, module finding. Resilience as cut hardness: a network tolerates \(k\) failures exactly when its minimum cut exceeds \(k\), which turns a vague resilience goal into a clean quantitative target.
- Cycle
- Graph theory and combinatorics. Cycles are foundational objects (Hamiltonian cycles, Eulerian circuits, the cycle space of a graph, girth), and properties such as robustness and planarity are decided by cycle structure.
This sourceGraduate Texts in Mathematics 244. New York: Springer, 2008. Standard reference for cycles as foundational graph objects: Hamiltonian cycles, Eulerian circuits, cycle space, girth, and their role in robustness and planarity.
- Graph theory and combinatorics. Cycles are foundational objects (Hamiltonian cycles, Eulerian circuits, the cycle space of a graph, girth), and properties such as robustness and planarity are decided by cycle structure.
- Single Point of Failure
- A network of N components has up to a quadratic number of possible dependencies, and tracing all of them is intractable.
This sourceStandard graph-theory text establishing that the complete graph on N vertices has N(N−1)/2 edges, so the number of possible pairwise dependencies is quadratic in N.
- A network of N components has up to a quadratic number of possible dependencies, and tracing all of them is intractable.
Domain-specific¶
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Not recorded. Neither this nor any other of the 5 citations of this work carries a recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
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Links previously used in the corpus¶
Before the registry existed this work was also linked 1 other way.
Registry ID ref:630c8f079bed · see in the full table