Pairwise temporal interactions between entities can be represented as temporal networks, which code the propagation of processes such as epidemic spreading or information cascades, evolving on top of them. The largest outcome of these processes is directly linked to the structure of the underlying network. Indeed, a node of a network at given time cannot affect more nodes in the future than it can reach via time-respecting paths. This set of nodes reachable from a source defines an out-component, which identification is costly. In this paper, we propose an efficient matrix algorithm to tackle this issue and show that it outperforms other state-of-the-art methods. Secondly, we propose a hashing framework to coarsen large temporal networks into smaller proxies on which out-components are easier to estimate, and then recombined to obtain the initial components. Our graph hashing solution has implications in privacy respecting representation of temporal networks.

翻译：实体间的成对时序交互可表示为时序网络，此类网络编码了在其上演化的传播过程（如流行病扩散或信息级联）的传播路径。这些过程的最大结果与底层网络结构直接相关。事实上，给定时刻的网络节点通过时间尊重路径能影响的未来节点数量受其可达性限制。从源节点出发的可达节点集合定义了外出分量，其识别代价高昂。本文提出了一种高效的矩阵算法来解决该问题，并证明其性能优于现有其他先进方法。其次，我们提出了一种哈希框架，将大规模时序网络粗化为更易估计外出分量的小型代理网络，再通过重组恢复原始分量。我们的图哈希解决方案对时序网络的隐私保护表示具有重要启示。