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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Estimating formation mechanisms and degree distributions in mixed attachment networks
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Estimating formation mechanisms and degree distributions in mixed attachment networks

机译：混合附件网络中的形成机制和程度分布

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摘要

Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to random and preferential linkage with a fixed probability. Past approaches apply likelihood analysis to estimate the probability of occurrence of each mechanism at a particular network instance, exploiting the concavity of the likelihood function at each point in time. However, the probability of connecting to existing nodes, and consequently the likelihood function itself, varies as networks grow. We establish conditions under which applying likelihood analysis guarantees the existence of a local maximum of the time-varying likelihood function and prove that an expectation maximization algorithm provides a convergent estimate. Furthermore, the in-degree distributions of the nodes in the growing networks are analytically characterized. Simulations show that, under the proposed conditions, expectation maximization and maximum-likelihood accurately estimate the actual contribution of each mechanism, and in-degree distributions converge to stationary distributions.
机译：我们的工作介绍了一种估算附着机制对成长网络形成的贡献的方法。我们提出了一种通用模型，其中通过根据具有固定概率的随机和优先链接的随机和优先链接来驱动增长。过去的方法适用似然分析来估计特定网络实例的每个机制的发生概率，利用在每个时间点处的似然函数的凹面。然而，连接到现有节点的概率以及因此似然函数本身的概率随着网络的增长而变化。我们建立了应用似然分析的条件，保证了存在局部最大的时变似然函数的存在，并证明期望最大化算法提供了会聚估计。此外，生长网络中的节点的程度分布在分析表征。模拟表明，在拟议的条件下，预期最大化和最大可能性准确地估计每个机制的实际贡献，以及程度的分布收敛到静止分布。

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