In this article, we discuss the random graph, Barabási–Albert (BA) model, and lattice networks from a unified view point, with the parameter ω with values \(1,0, - 1\) characterizing these networks, respectively. The parameter is related to the preferential attachment of nodes in the networks and has different weights for the incoming and outgoing links. In addition, we discuss the correspondence between quantum statistics and the networks. Positive and negative ω correspond to Bose and Fermi-like statistics, respectively, and we obtain the distribution that connects the two. When ω is positive, it is related to the threshold of Bose–Einstein condensation (BEC). As ω decreases, the area of the BEC phase is narrowed, and disappears in the limit ω = 0. When ω is negative, nodes have limits in the number of attachments for newly added nodes (outgoing links), which corresponds to Fermi statistics. We also observe the Fermi degeneracy of the network. When ω = −1, a standard Fermion-like network is observed. Fermion networks are realized in the cryptocurrency network “Tangle”.

中文翻译：

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玻色子和费米子之间非对称优先连接节点的量子统计和网络

在本文中，我们从统一的角度讨论随机图、Barabási-Albert (BA) 模型和晶格网络，参数ω取值\(1,0, - 1\)分别表征这些网络。该参数与网络中节点的优先连接有关，对传入和传出链路具有不同的权重。此外，我们讨论了量子统计与网络之间的对应关系。正负ω分别对应玻色和类费米统计，我们得到了连接两者的分布。当ω为正时，它与玻色-爱因斯坦凝聚（BEC）的阈值有关。随着ω减小，BEC 相的面积变窄，并在极限ω = 0 内消失。当ω为负，节点对新添加节点（传出链接）的附件数量有限制，这对应于费米统计。我们还观察到网络的费米简并性。当ω = -1 时，观察到标准的费米子类网络。费米子网络是在加密货币网络“Tangle”中实现的。