识别网络增长中的时间依赖性
Identifying time dependence in network growth
摘要：
在真实网络中识别幂律缩放--表明偏好连接--已被证明是有争议的。批评者认为，在寻找偏好连接时，直接测量网络的时间演化比测量度分布更好。然而，许多已建立的方法不考虑任何潜在的时间依赖性的增长网络的附件内核，或方法假设节点度是关键的可观察到的决定网络的演变。在本文中，我们认为，这些假设可能会导致误导性的结论不断增长的网络的演变。我们通过引入Barab{á}si-Albert模型的一个简单适应来说明这一点，即“k2模型”，其中新节点与现有网络中的节点成比例地连接到距离目标节点一步或两步的节点数量。k2模型导致了依赖于时间的度分布和连接核，尽管最初似乎是线性优先连接，并且不需要在关键网络参数（例如平均出度）中包含显式的时间依赖性。我们发现，在几个真实世界的网络中，恒定的网络增长规则并不能描述它们的演变，也可以看到类似的效果。这意味着真实网络中特定度分布的度量也可能随着时间的推移而变化。
英文摘要：
Identifying power-law scaling in real networks - indicative of preferential attachment - has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution when looking for preferential attachment. However, many of the established methods do not account for any potential time-dependence in the attachment kernels of growing networks, or methods assume that node degree is the key observable determining network evolution. In this paper, we argue that these assumptions may lead to misleading conclusions about the evolution of growing networks. We illustrate this by introducing a simple adaptation of the Barab{á}si-Albert model, the "k2 model", where new nodes attach to nodes in the existing network in proportion to the number of nodes one or two steps from the target node. The k2 model results in time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment, and without the need to include explicit time dependence in key network parameters (such as the average out-degree). We show that similar effects are seen in several real world networks where constant network growth rules do not describe their evolution. This implies that measurements of specific degree distributions in real networks are also likely to change over time.
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