On leaders and condensates in a growing network
On leaders and condensates in a growing network
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关于不断增长的网络中的领导者和凝聚体
DOI：
10.1088/1742-5468/2010/07/p07031
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
J. Luck
中科院分区：
文献类型：
--
作者：
C. Godrèche;J. Luck
不断增长的网络的斑马军团-巴拉巴西模式被重新审视。该模型由一个优先连接规则定义，该规则同时涉及节点的度数及其固有配合度，它的基本性质是在某个有限的临界温度以下经历到凝聚相的相变，以适当地选择配合度分布。在高温下，它表现出与巴拉巴西-阿尔伯特模型的交叉，而在低温下，健身环境变得非常崎岖，与最近引入的创纪录的增长过程交叉。我们首先对领导者的历史进行了分析，领导者被定义为在给定时间具有最大度的节点。在一般的有限温度体系中，新的领导者无休止地出现，尽管是在双对数时间尺度上，即极其缓慢。然后，我们给出了一幅凝聚相中动力学的新图景。后者的特点是凝析油具有无限的层次结构，其大小不是自我平均的，并且永远保持波动。
The Bianconi–Barabási model of a growing network is revisited. This model, defined by a preferential attachment rule involving both the degrees of the nodes and their intrinsic fitnesses, has the fundamental property of undergoing a phase transition to a condensed phase below some finite critical temperature, for an appropriate choice of the distribution of fitnesses. At high temperature it exhibits a crossover to the Barabási–Albert model, and at low temperature, where the fitness landscape becomes very rugged, a crossover to the recently introduced record-driven growth process. We first present an analysis of the history of leaders, the leader being defined as the node with largest degree at a given time. In the generic finite-temperature regime, new leaders appear endlessly, albeit on a doubly logarithmic timescale, i.e., extremely slowly. We then give a novel picture of the dynamics in the condensed phase. The latter is characterized by an infinite hierarchy of condensates, whose sizes are non-self-averaging and keep fluctuating forever.