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Preferential attachment with power law growth in the number of new edges

机译：在新边缘的数量中优惠依附权力法生长

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The Barabasi-Albert model is used to explain the formation of power laws in the degree distributions of networks. The model assumes that the principle of preferential attachment underlies the growth of networks, that is, new nodes connects to a fixed number of nodes with a probability that is proportional to their degrees. Yet, for empirical networks the number of new edges is often not constant, but varies as more nodes become part of the network. This paper considers an extension to the original Barabasi-Albert model, in which the number of edges established by a new node follows a power law distribution with support in the total number of nodes. While most new nodes connect to a few nodes, some new nodes connect to a larger number. We first characterize the dynamics of growth of the degree of the nodes. Second, we identify sufficient conditions under which the expected value of the average degree of the network is asymptotically stable. Finally, we show how the dynamics of the model resemble the evolution of protein interaction networks, Twitter, and Facebook.
机译：BaraBasi-Albert模型用于解释网络的程度分布在网络中的形成。该模型假设优先附件原理基础是网络的生长，即新节点连接到具有与其度成比例的概率的固定数量的节点。然而，对于经验网络，新边缘的数量通常不是恒定的，而是随着更多节点成为网络的一部分而变化。本文考虑了原始Barabasi-Albert模型的扩展，其中新节点建立的边缘的数量跟随电源法分布，在节点的总数中都有支持。虽然大多数新节点连接到几个节点，但一些新节点连接到更大的数字。我们首先表征节点的增长的动态。其次，我们确定了足够的条件，其中网络平均程度的预期值是渐近稳定的。最后，我们展示了模型的动态方式如何类似于蛋白质互动网络，推特和Facebook的演变。

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