论文标题
复杂网络中的$ k $ core和社区结构之间的相互作用
Interplay between $k$-core and community structure in complex networks
论文作者
论文摘要
在集合中至少具有$ k $邻居的最大节点中的网络组织，称为$ k $ core分解，已用于研究各种现象。已经表明，最内向的$ k $ shells中的节点在传染过程，共识的出现和系统的弹性中起着至关重要的作用。众所周知，许多经验网络的$ K $ - 核分解不能用单独的每个节点的程度或等效的随机图模型来解释，以保留每个节点的程度（即配置模型）。在这里，我们研究了某些经验网络的$ K $ - 核分解以及某些随机的对应物的分解，并研究网络的$ K $ shell结构可以由社区结构解释到多大程度上。我们发现，在随机化过程中保留社区结构对于生成$ k $ core分解与经验的网络至关重要。我们还强调了在某些网络中的存在，在最内向的$ k $ shells中的浓度集中在少数社区中。
The organisation of a network in a maximal set of nodes having at least $k$ neighbours within the set, known as $k$-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $k$-shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the $k$-core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the $k$-core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the $k$-shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose $k$-core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost $k$-shells into a small number of communities.
