[论文解读] Effects of time window size and placement on the structure of aggregated networks

Gautier Krings, Márton Karsai+3 more|arXiv (Cornell University)|Feb 6, 2012

Complex Network Analysis Techniques参考文献 20被引用 17

一句话总结

本研究利用匿名化的移动通话记录，探究时间窗口大小与位置对聚合时序网络结构特性的影响。研究发现，社区结构约在1周内形成，度分布与权重分布的稳定性在数天至数周内达成，而30天窗口能产生最稳定的网络结构；更长的窗口则会放大弱连接与随机连接的影响。

ABSTRACT

Complex networks are often constructed by aggregating empirical data over time, such that a link represents the existence of interactions between the endpoint nodes and the link weight represents the intensity of such interactions within the aggregation time window. The resulting networks are then often considered static. More often than not, the aggregation time window is dictated by the availability of data, and the effects of its length on the resulting networks are rarely considered. Here, we address this question by studying the structural features of networks emerging from aggregating empirical data over different time intervals, focussing on networks derived from time-stamped, anonymized mobile telephone call records. Our results show that short aggregation intervals yield networks where strong links associated with dense clusters dominate; the seeds of such clusters or communities become already visible for intervals of around one week. The degree and weight distributions are seen to become stationary around a few days and a few weeks, respectively. An aggregation interval of around 30 days results in the stablest similar networks when consecutive windows are compared. For longer intervals, the effects of weak or random links become increasingly stronger, and the average degree of the network keeps growing even for intervals up to 180 days. The placement of the time window is also seen to affect the outcome: for short windows, different behavioural patterns play a role during weekends and weekdays, and for longer windows it is seen that networks aggregated during holiday periods are significantly different.

研究动机与目标

• 理解聚合时间窗口的长度与位置如何影响实证时序网络的结构特征。
• 识别关键网络属性（如聚类系数、度分布和连通性）在何种时间尺度下趋于稳定或发生显著变化。
• 确定是否存在一个最优的聚合窗口，能够最好地捕捉人类通信网络中重复出现且稳定的网络特征。
• 研究行为模式（如工作日与周末、节假日期间）通过窗口位置效应在塑造网络结构中的作用。

提出的方法

• 将比利时某运营商6个月内的聚合时间戳移动通话记录，采用不同时间窗口聚合为静态网络。
• 计算标准网络指标：聚类系数、平均度、度分布与权重分布，以及最大连通分量的大小。
• 比较不同长度的连续非重叠时间窗口，评估其结构相似性与稳定性。
• 通过分析链接权重分布与邻域重叠，评估社区结构的出现情况。
• 比较工作日、周末与节假日期间网络结构的差异，评估窗口位置的影响。
• 使用缩放后的分布识别底层过程在不同时间尺度下的平稳性。

实验结果

研究问题

• RQ1 在何种时间窗口长度下，聚类系数与度分布等关键网络属性趋于稳定？
• RQ2 聚合窗口的位置（如工作日与周末、节假日期与非节假日期）如何影响生成的网络结构？
• RQ3 何种时间窗口长度能产生在连续时间间隔中结构最相似且最稳定的网络？
• RQ4 在聚合过程中，由强而重复的链接驱动的社区结构最早可在何时被检测到？
• RQ5 随着聚合窗口变长，弱连接或随机连接（如一次性通话）在多大程度上会扭曲网络结构？

主要发现

• 聚类系数在约9天时达到峰值，表明社区结构在约1周的聚合时间内开始显现。
• 度分布与权重分布分别在约3天和3周后趋于平稳，表明基本网络统计量在早期即实现稳定。
• 以30天为窗口聚合的网络与连续窗口之间的结构相似性最高，表明在此时间尺度下网络结构最稳定。
• 当聚合区间超过30天时，平均度持续增长，表明弱连接或随机连接的影响不断增强。
• 周末通话模式导致最大连通分量的增长速度慢于工作日，表明工作日通话可能起到拓扑捷径的作用。
• 节假日期间聚合的网络结构与非节假日期间存在显著差异，凸显了行为模式变化对网络结构的影响。