复杂网络中的“丛聚”混合
"Clumpiness" Mixing in Complex Networks
摘要：
介绍了复杂网络簇性的三种度量方法。这些措施量化了网络的大多数中心节点如何聚集在一起。在以前的研究中定义的扩散系数测量了类似的特征，但只考虑了直接相互连接的中心节点的聚集性。本文中定义的聚集系数也考虑了中心节点被几个链接分开的情况。该定义基于节点度和节点对之间的距离。集块系数和扩散系数可以定义四类网络。数值计算表明，该分类方案成功地将30个真实世界的网络分为四类：丛生的排斥，丛生的排斥，松散的排斥和松散的排斥网络。聚类系数也区分了Erdos-Renyi模型和Barabasi-Albert模型，而聚类系数不能区分两者。此外，还讨论了块度系数的界以及三种块度测度之间的关系。
英文摘要：
Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic, but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by a few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of network. Numerical calculations demonstrate that the classification scheme successfully categorizes 30 real-world networks into the four classes: clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdos-Renyi model from the Barabasi-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relationships between the three measures of clumpiness are discussed.
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