arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2005.01147physics.soc-phcs.SI
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复杂网络中$k$ -核与社团结构的相互作用

Interplay between $k$-core and community structure in complex networks

Irene Malvestio, Alessio Cardillo, Naoki Masuda

摘要:

在一个最大的一组节点中的网络的组织,至少有$k$邻居的集合内,被称为$k$核心分解,已被用于研究各种现象。研究表明,最内层$k$壳层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$k$ -核心分解不能单独用每个节点的度来解释,或者等价地,不能用保持每个节点的度的随机图模型来解释(即,配置模型)。在这里,我们研究的$k$核心分解的一些经验网络,以及一些随机的同行,并检查在何种程度上的$k$壳结构的网络可以解释的社区结构。我们发现,在随机化过程中保持社区结构是至关重要的生成网络的$k$核心分解是接近的经验。我们还强调存在,在一些网络中,集中的节点在最里面的$k$ -壳到少数社区。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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