A temporal network is a dynamic graph where every edge is assigned an integer time label that indicates at which discrete time step the edge is available. We consider the problem of hierarchically decomposing the network and introduce an edge-based decomposition framework that unifies the core and truss decompositions for temporal networks while allowing us to consider the network's temporal dimension. Based on our new framework, we introduce the $(k,\Delta)$-core and $(k,\Delta)$-truss decompositions, which are generalizations of the classic $k$-core and $k$-truss decompositions for multigraphs. Moreover, we show how $(k,\Delta)$-cores and $(k,\Delta)$-trusses can be efficiently further decomposed to obtain spatially and temporally connected components. We evaluate the characteristics of our new decompositions and the efficiency of our algorithms. Moreover, we demonstrate how our $(k,\Delta)$-decompositions can be applied to analyze malicious content in a Twitter network to obtain insights that state-of-the-art baselines cannot obtain.

翻译：时序网络是一种动态图，其中每条边都被分配了一个整数时间标签，用以指示该边在哪个离散时间步可用。我们考虑了网络的层次分解问题，并引入了一种基于边的分解框架，该框架统一了时序网络的核心分解与核分解，同时允许我们考虑网络的时间维度。基于我们的新框架，我们引入了$(k,\Delta)$-核心分解与$(k,\Delta)$-核分解，它们是对多重图经典$k$-核心分解与$k$-核分解的推广。此外，我们展示了如何进一步高效地分解$(k,\Delta)$-核心与$(k,\Delta)$-核，以获得空间和时间上连通的组件。我们评估了新分解方法的特性以及我们算法的效率。此外，我们演示了如何将$(k,\Delta)$-分解应用于分析Twitter网络中的恶意内容，以获得现有最先进基线方法无法获得的洞察。