论文标题
确定时间依赖网络增长
Identifying time dependence in network growth
论文作者
论文摘要
事实证明，在实际网络中识别幂律缩放（表明优先附件）已被证明是有争议的。批评家认为，直接测量网络的时间演变要比在寻找优先依恋时测量度分布更好。但是，许多已建立的方法并未解释增长网络的附件内核中的任何潜在时间依赖性，或者假设节点度是确定网络演变的关键。在本文中，我们认为这些假设可能会导致关于不断增长的网络演变的误导性结论。我们通过引入barab {Á} Si-Albert模型的简单改编“ K2模型”来说明这一点，其中新节点附加到现有网络中的节点，这是与距目标节点一两个步骤的节点的数量成正比的。 K2模型导致时间依赖性度分布和附件内核，尽管最初似乎会增长为线性优先附件，而无需将显式时间依赖性包含在关键网络参数中（例如平均值外数）。我们表明，在恒定的网络增长规则没有描述其演变的几个现实世界网络中也可以看到类似的效果。这意味着实际网络中特定程度分布的测量也可能会随着时间而变化。
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.
