Abstract With the rapid development of science and technology, the world is becoming increasingly connected. The following dire need for understanding both the relationships amongst individuals and the global structural characteristics brings forward the study of network sciences and many interdisciplinary subjects in recent years. As a result, it is crucial to have methods and algorithms that help us to unveil the structural properties of a network. Over the past few decades, many essential algorithms have been developed by scientists from many different fields. This review will focus on one of the most widely used methods called the k -core decomposition. The k -core decomposition is to find the largest subgraph of a network, in which each node has at least k neighbors in the subgraph. The most commonly used algorithm to perform k -core decomposition is a pruning process that to recursively remove the nodes that have degrees less than k . The algorithm was firstly proposed by Seidman in 1983 and soon became one of the most popular algorithms to detect the network structure due to its simplicity and broad applicability. This algorithm is widely adopted to find the densest part of a network across a broad range of scientific subjects including biology, network science, computer science, ecology, economics, social sciences, etc., so to achieve the vital knowledge under different contexts. Besides, a few physicists find that an exciting phase transition emerges with various critical behaviors during the pruning process. 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.

中文翻译：

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k-core：理论与应用

摘要 随着科学技术的飞速发展，世界的联系日益紧密。对理解个体之间的关系和全局结构特征的迫切需要提出了近年来对网络科学和许多交叉学科的研究。因此，拥有帮助我们揭示网络结构特性的方法和算法至关重要。在过去的几十年里，许多不同领域的科学家开发了许多基本算法。本次审查将重点介绍一种最广泛使用的方法，称为 k 核分解。k核分解是寻找网络的最大子图，其中每个节点在子图中至少有k个邻居。执行 k 核分解最常用的算法是修剪过程，它递归地删除度数小于 k 的节点。该算法由 Seidman 于 1983 年首次提出，由于其简单性和广泛的适用性，很快成为最流行的网络结构检测算法之一。该算法被广泛用于在生物学、网络科学、计算机科学、生态学、经济学、社会科学等广泛的科学学科中寻找网络中最密集的部分，从而获得不同背景下的重要知识。此外，一些物理学家发现在修剪过程中会出现令人兴奋的相变，并伴随着各种关键行为。