随机和混合花图
Stochastic and mixed flower graphs
摘要：
随机性被引入到一类研究得很好的递归生长图：$(u,v)$花网，它具有幂律度分布以及小世界属性（当$u=1$）。随机变量在不同的（确定性的）花图之间插值，可能更好地模拟真实世界的网络。然而，所涉及的随机乘法增长过程导致网络的传播系综，其链路、节点和环路的数量具有有限的方差。然而，度指数和回路指数在无穷大图的热力学极限下达到唯一值。我们还研究了一类混合花网络，密切相关的随机花，但它是在一个确定性的方式递归增长。混合花网的确定性增长消除了集成传播，其递归增长允许精确分析其（唯一定义的）混合属性。
英文摘要：
Stochasticity is introduced to a well studied class of recursively grown graphs: $(u,v)$-flower nets, which have power-law degree distributions as well as small-world properties (when $u=1$). The stochastic variant interpolates between different (deterministic) flower graphs and might better model real-world networks. The random multiplicative growth process involved, however, leads to a spread ensemble of networks with finite variance for the number of links, nodes, and loops. Nevertheless, the degree exponent and loopiness exponent attain unique values in the thermodynamic limit of infinitely large graphs. We also study a class of mixed flower networks, closely related to the stochastic flowers, but which are grown recursively in a deterministic way. The deterministic growth of mixed flower-nets eliminates ensemble spreads, and their recursive growth allows for exact analysis of their (uniquely defined) mixed properties.
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