In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most . That is, some vertex in the subgraph touches or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of for which it is -degenerate.

Jun 5, 2023 · In graph theory, the K-Core of a graph is a maximal subgraph in which every vertex has at least degree . K-Cores are used to identify the most tightly connected parts of a graph and can provide insights into the overall structure and behavior of a network.

Jun 8, 2021 · k-Core算法是一种子图挖掘算法，用于寻找一个图中符合指定核心度的顶点的集合，即要求每个顶点至少与该子图中的其他k个顶点相关联。 如图1所示，分别对应1-Core，2-Core和3-Core，任何一个图，在不包含孤立顶点的情况下，都是1-Core的。 k-Core算法的过程也是非常简单的，一共分为两步，其实两步所做的内容是一样的，至于为什么要分两步执行同一个过程，可以自行思考一下。 Step 1： 将图G中度数小于k的顶点全部移除，得到子图G'。 Step 2： 将图G' …

Mar 27, 2023 · The standard algorithm to find a k-core graph is to remove all the vertices that have degree less than- ‘K’ from the input graph. We must be careful that removing a vertex reduces the degree of all the vertices adjacent to it, hence the degree of adjacent vertices can also drop below-‘K’.

Nov 10, 2019 · In general, the k -core of a network is the maximal subgraph in which each node has at least k connections to other nodes in the subgraph, despite how many links we have outside the subgraph.

k-core appears suddenly when m reaches c kn/2; here c k = min λ>0 λ/π k(λ) and π k(λ) = P{Poisson(λ) ≥ k − 1}. In particular, c 3 ≈ 3.35. We also demonstrate that, unlike the 2-core, when a k-core appears for the first time it is very likely to be giant, of size ≈ p k(λ k)n. Here λ k is the minimum point of λ/π k(λ) and p k ...

Returns the k-core of G. A k-core is a maximal subgraph that contains nodes of degree k or more. Deprecated since version 3.3: k_core will not accept MultiGraph objects in version 3.5.

Apr 8, 2025 · The k-cores of a graph are the connected components that remain after all vertices of vertex degree less than k have been repeatedly removed. The largest value k such that a graph G has a k-core is called the graph degeneracy of G.

This review aims at filling the gap by making a comprehensive review of the theoretical advances on k-core decomposition problem, along with a review of a few applications of the k-core decomposition from many interdisciplinary perspectives.

The K-core decomposition constitutes a process of separates the nodes in a graph into groups based on the degree sequence and topology of the graph. The term i-core refers to a maximal subgraph of the original graph such that each node in this subgraph has degree at least i.