Non-Altering Time Scales for Aggregation of Dynamic Networks into Series of Graphs

Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets $(u,v,t)$ where $u$ and $v$ are two nodes having a link between them at time $t$. A very large number of studies on these objects start by aggregating the data in disjoint time windows of length $\Delta$ in order to obtain a series of graphs on which are made all subsequent analyses. Here we are concerned with the impact of the chosen $\Delta$ on the obtained graph series. We address the fundamental question of knowing whether a series of graphs formed using a given $\Delta$ faithfully describes the original link stream. We answer the question by showing that such dynamic networks exhibit a threshold for $\Delta$, which we call the \emph{saturation scale}, beyond which the properties of propagation of the link stream are altered, while they are mostly preserved before. We design an automatic method to determine the saturation scale of any link stream, which we apply and validate on several real-world datasets.