随机临界分枝树的离散性
Disassortativity of random critical branching trees
摘要：
随机临界分枝树（CBTs）是由乘法分枝过程生成的，其中分枝数是随机确定的，与其祖先的度无关。在这里，我们分析表明，尽管这种随机的独立性，存在度度相关性（DDC）的CBT，它是discretionative。此外，分形网络的骨架，由边介数中心形成的最大生成树，表现出类似于DDC中的CBT。这个解析解和观察结果支持了复杂网络的分形标度起源于DDC中的离散性的论点。
英文摘要：
Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.
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