Matjaž Zaveršnik is a mathematician whose work with Vladimir Batagelj includes an efficient algorithm for finding all k-cores of networks. Their paper presents a method whose running time is linear in the number of edges for the networks considered, making the decomposition practical on large inputs.[ref]
https://arxiv.org/abs/cs/0310049. An O(m) Algorithm for Cores Decomposition of Networks, authors and abstract
The key structural object is a k-core: a maximal induced subgraph whose minimum degree is at least . Assigning each vertex its largest such provides a compact description of its position within nested connected regions; a high value records local connectivity rather than merely a large original degree.Biographical record: www2.arnes.si/~sspmgiac/mirk2003/Zbornik.pdf
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