The core decomposition of networks has attracted significant attention due to its numerous applications in real-life problems. Simply stated, the core decomposition of a network (graph) assigns to each graph node v, an integer number c(v) (the core number), capturing how well v is connected with respect to its neighbors. This concept is strongly related to the concept of graph degeneracy, which has a long history in graph theory. Although the core decomposition concept is extremely simple, there is an enormous interest in the topic from diverse application domains, mainly because it can be used to analyze a network in a simple and concise manner by quantifying the significance of graph nodes. Therefore, there exists a respectable number of research works that either propose efficient algorithmic techniques under different settings and graph types or apply the concept to another problem or scientific area. Based on this large interest in the topic, in this survey, we perform an in-depth discussion of core decomposition, focusing mainly on: (i) the basic theory and fundamental concepts, (ii) the algorithmic techniques proposed for computing it efficiently under different settings, and (iii) the applications that can benefit significantly from it.

中文翻译：

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网络的核心分解：理论，算法和应用

网络的核心分解由于其在现实生活中的大量应用而引起了广泛的关注。简而言之，网络（图）的核心分解为每个图节点v分配一个整数c（v）（核心号），以捕获v相对于其邻居的连接程度。这个概念与图退化的概念密切相关，在图论方面有着悠久的历史。尽管核心分解概念非常简单，但是来自不同应用领域的该主题引起了极大兴趣，主要是因为它可以通过量化图节点的重要性以一种简洁的方式来分析网络。因此，存在大量的研究工作，这些工作要么提出了在不同设置和图形类型下的有效算法技术，要么将该概念应用于另一个问题或科学领域。基于对这一主题的极大兴趣，在本次调查中，我们对核心分解进行了深入的讨论，主要集中在：（i）基本理论和基本概念，（ii）提出了在以下条件下有效计算它的算法技术不同的设置，