按节点属性抽样网络
Sampling networks by nodal attributes
摘要：
在社交网络中，个体或节点通过每次选择一个通信渠道来连接到其他节点，以重新建立现有的社交链接。由于可用的数据集通常限于有限数量的通道或层，这些节点的自主决策过程构成了多路复用网络的采样，导致由节点的行为引起的采样偏差的一个（尽管非常重要）示例。我们开发了一个通用的设置，以获得洞察力和理解的网络采样模型，其中采样的概率在原始网络中的链接取决于其相邻节点的属性$h$的类。假设节点属性独立地从任意分布$ρ(h)$中提取，并且节点属性$h_i$和$h_j$的链路$ij$的采样概率$r(h_i , h_j)$也是任意的，我们推导出采样网络的度分布、度相关性和聚类谱等网络特性的精确解析表达式。采样网络的性质是原始网络拓扑的数量之和，由采样产生的因子加权。基于我们的分析，我们发现采样网络可能具有原始网络中不存在的采样诱导网络属性，这意味着将样本结果天真地推广到整个原始网络的潜在风险。我们还考虑的情况下，当相邻节点的相关属性，以显示如何推广我们的形式主义，这样的采样偏差，我们得到了很好的分析结果和数值模拟之间的协议。
英文摘要：
In a social network individuals or nodes connect to other nodes by choosing one of the channels of communication at a time to re-establish the existing social links. Since available data sets are usually restricted to a limited number of channels or layers, these autonomous decision making processes by the nodes constitute the sampling of a multiplex network leading to just one (though very important) example of sampling bias caused by the behavior of the nodes. We develop a general setting to get insight and understand the class of network sampling models, where the probability of sampling a link in the original network depends on the attributes $h$ of its adjacent nodes. Assuming that the nodal attributes are independently drawn from an arbitrary distribution $ρ(h)$ and that the sampling probability $r(h_i , h_j)$ for a link $ij$ of nodal attributes $h_i$ and $h_j$ is also arbitrary, we derive exact analytic expressions of the sampled network for such network characteristics as the degree distribution, degree correlation, and clustering spectrum. The properties of the sampled network turn out to be sums of quantities for the original network topology weighted by the factors stemming from the sampling. Based on our analysis, we find that the sampled network may have sampling-induced network properties that are absent in the original network, which implies the potential risk of a naive generalization of the results of the sample to the entire original network. We also consider the case, when neighboring nodes have correlated attributes to show how to generalize our formalism for such sampling bias and we get good agreement between the analytic results and the numerical simulations.
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