非演化网络中与富俱乐部系数相关的系综
Ensembles related to the rich-club coefficient for non-evolving networks
摘要：
在复杂网络中，富节点是度高的节点的子集。这些连接良好的节点往往主导网络结构的组织。在非进化网络中，参考网络被用来检测富节点之间的连接是偶然的还是由未知的机制引起的。机会被表示为从网络集合获得的参考网络。当与原始网络相比时，参考网络折扣表明存在一个超越结构限制的良好连接的富人俱乐部。在这里，我们修改了一些属性的合奏只保存度分布，并引入了两个新的参考网络来研究丰富的节点作为网络结构的组织者的重要性。第一个参考网络是从一个网络集合中获得的，其中集合中的所有成员都具有相同的富俱乐部系数。从系综中得到的参考网络是独立的。我们建议，这个参考网络可以用来研究网络的非对称性是一个基本属性，在许多社交网络的常见情况。第二个参考网络是从一个集合中获得的，其中该集合的成员都具有相同的概率度分布和富俱乐部系数。从该集合获得的参考网络具有与原始网络非常相似的结构。这个集合可以用来量化富节点之间的相关性，并确定哪些链路是网络结构的骨干。
英文摘要：
In complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if the connectivity between the rich nodes is due to chance or caused by an unknown mechanism. Chance is represented as a reference network obtained from an ensemble of networks. When compared with the original network the reference network discounts suggests the existence of a well connected rich club beyond structural constraints. Here we revise some of the properties of the ensemble obtained by conserving only the degree distribution and introduce two new reference networks to study the importance of the rich nodes as organisers of the network structure. The first reference network is obtained from an ensemble of networks where all the members of the ensemble have the same rich--club coefficient. The reference network obtained from the ensemble is assortative. We propose that this reference network can be used to study networks where assortativness is a fundamental property, a common case in many social networks. The second reference network is obtained from an ensemble where the members of the ensemble all have the same probability degree distribution and rich-club coefficient. The reference network obtained from this ensemble has a very similar structure to the original network. This ensemble can be used to quantify correlations between the rich nodes and pinpoint which links are the backbone of the network's structure.
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。
