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摘要翻译：
我们研究了一组孤立的地节点在每一个时间步长增加一个新节点的情况下网络的增长，以及从新节点到随机选择的已有节点的固定数量的有向边的增长。使用固定宽度的时间窗口，以便通常只有在最近窗口内进入网络的节点可以接收新的传入边缘。由此产生的有向网络在任何时候都是非循环的，并且允许一些地面节点，然后称为接收器，从一些非地面节点到达。我们把这种网络看作是部分有序成分的抽象系统的代表，例如在与技术进化有关的一些领域。感兴趣的两个性质是可以从随机选择的非地面节点到达的接收器的数目（它的到达范围），对于固定的接收器，在给定时间，从最近进入网络的一些节点可以到达接收器的不重叠的有向路径的数目。我们通过模拟和解析特性证明了到达率是按幂律分布的，期望的有向路径的数目很少，这可能表明在网络增长过程的后期恢复接收器对意外的路径中断非常敏感。
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英文标题：
《Reachability and recoverability of sink nodes in growing acyclic
directed networks》
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作者：
Valmir C. Barbosa
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We study the growth of networks from a set of isolated ground nodes by the addition of one new node per time step and also of a fixed number of directed edges leading from the new node to randomly selected nodes already in the network. A fixed-width time window is used so that, in general, only nodes that entered the network within the latest window may receive new incoming edges. The resulting directed network is acyclic at all times and allows some of the ground nodes, then called sinks, to be reached from some of the non-ground nodes. We regard such networks as representative of abstract systems of partially ordered constituents, for example in some of the domains related to technological evolution. Two properties of interest are the number of sinks that can be reached from a randomly chosen non-ground node (its reach) and, for a fixed sink, the number of nonoverlapping directed paths through which the sink can be reached, at a given time, from some of the latest nodes to have entered the network. We demonstrate, by means of simulations and also of analytic characterizations, that reaches are distributed according to a power law and that the desired directed paths are expected to occur in very small numbers, perhaps indicating that recovering sinks late in the process of network growth is strongly sensitive to accidental path disruptions.
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PDF链接：
https://arxiv.org/pdf/706.3805
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