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普遍认为k-core概念由Seidman<ref name= 'k-core concept'>{{Cite journal| doi = 10.1016/0378-8733(83)90028-X| issn = 03788733| volume = 5| issue = 3| pages = 269–287| last = Seidman| first = Stephen B.| title = Network structure and minimum degree| journal = Social Networks| year= 1983| url = https://linkinghub.elsevier.com/retrieve/pii/037887338390028X}}</ref>首次提出，对于给定的网络，递归删除网络中度数小于k的节点可以得到网络的极大子图，其中每个节点的度数不小于k（不考虑子图外的连接情况），该子图为原网络的k-core。与k-core密切相关的概念还包括:

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:* k-shell<ref name='k-shell'> {Cite journal| doi = 10.1073/pnas.0701175104| issn = 0027-8424, 1091-6490| volume = 104| issue = 27| pages = 11150–11154| last1 = Carmi| first1 = Shai| last2 = Havlin| first2 = Shlomo| last3 = Kirkpatrick| first3 = Scott| last4 = Shavitt| first4 = Yuval| last5 = Shir| first5 = Eran| title = A model of Internet topology using <i>k</i> -shell decomposition| journal = Proceedings of the National Academy of Sciences|date = 2007-07-03| url = https://pnas.org/doi/full/10.1073/pnas.0701175104}}</ref>：属于k-core，但不属于(k+1)-core的点集，通过k-core分解过程可以将网络根据k-shell进行分层。

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:* k-shell<ref name='k-shell'> {{Cite journal| doi = 10.1073/pnas.0701175104| issn = 0027-8424, 1091-6490| volume = 104| issue = 27| pages = 11150–11154| last1 = Carmi| first1 = Shai| last2 = Havlin| first2 = Shlomo| last3 = Kirkpatrick| first3 = Scott| last4 = Shavitt| first4 = Yuval| last5 = Shir| first5 = Eran| title = A model of Internet topology using <i>k</i> -shell decomposition| journal = Proceedings of the National Academy of Sciences|date = 2007-07-03| url = https://pnas.org/doi/full/10.1073/pnas.0701175104}}</ref>：属于k-core，但不属于(k+1)-core的点集，通过k-core分解过程可以将网络根据k-shell进行分层。

:* k-crust：从1到k的k-shell的并集，代表网络的外围结构

:* k-corona：k-core中度数恰好为k的节点组成的点集

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K-core (查看源代码)

2025年6月15日 (日) 10:03的版本