Cores, shell indices and the degeneracy of a graph limit
arXiv:1805.03736
Abstract
The -core of a graph is the maximal subgraph in which every node has degree at least~, the shell index of a node is the largest such that the -core contains the node, and the degeneracy of a graph is the largest shell index of any node. After a suitable normalization, these three concepts generalize to limits of dense graphs (also called graphons). In particular, the degeneracy is continuous with respect to the cut metric.
11 pages including appendix, no figure